BA6933 WEEK6 QUIZZIES CHAPTER 13 AND 14 QUIZZIES

Part of an ANOVA table is shown below.

a. SSE/(nT - k).

b. SSE/(k - 1).

c. SSTR/k.

d. SSTR/(nT - k).

Hide Feedback

Correct

Solution

Correct Response 

a

 

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	180	3
Within Treatments (Error)
TOTAL	480	18

The mean square due to error (MSE) is

a. 20.

b. 15.

c. 60.

d. 18.

Hide Feedback

Correct

Solution

Correct Response

a

An ANOVA procedure for a two-factor factorial experiment produced the following: a = 6, b= 2, r = 2, SSA = 1.05, SSB = 16.67, SSAB = .60, and SST = 94.52. What is the value of the test statistic for determining whether there is a main effect for factor A?

a. .03

b. 2.63

c. The test statistic cannot be computed because SSE is not given.

d. .02

Hide Feedback

Correct

Solution

Correct Response

a

In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were assigned to each of the three methods. The time required to complete the task was recorded. The following information is provided: MSTR = 45.89 and MSE = 6.27. What is the critical value of F if we want to determine whether the means of the three populations are equal at the 5% level of significance?

a. 3.35

b. 2.93

c. 7.32

d. 1.96

Hide Feedback

Correct

Solution

Correct Response

a

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The number of degrees of freedom corresponding to between-treatments is

a. 5.

b. 60.

c. 4.

d. 59.

Hide Feedback

Correct

Solution

Correct Response

c

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as

a. main effect.

b. interaction.

c. error.

d. replication.

Hide Feedback

Correct

Solution

Correct Response

b

A completely randomized design is useful when the experimental units are

a. clustered.

b. stratified.

c. heterogeneous.

d. homogeneous.

Hide Feedback

Incorrect

Solution

Correct Response

d

In a factorial experiment, if there are x levels of factor A and y levels of factor B, there is a total of

a. xy treatment combinations.

b. (x + y)/2 treatment combinations.

c. 2(x + y) treatment combinations.

d. x + y treatment combinations.

Hide Feedback

Correct

Solution

Correct Response

a

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The sum of squares due to error (SSE) is

a. 1000.

b. 200.

c. 1600.

d. 600.

Hide Feedback

Correct

Solution

Correct Response

d

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment		Observations
A	20	30	25	33
B	22	26	20	28
C	40	30	28	22

The null hypothesis is to be tested at the 1% level of significance. The p-value is

a. greater than .1.

b. less than .01.

c. between .05 to .10.

d. between .01 to .025.

Hide Feedback

Correct

Solution

Correct Response

a

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is

a. 3.20.

b. 2.28.

c. 3.64.

d. 3.33.

Hide Feedback

Correct

Solution

Correct Response

a

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The mean square due to treatments (MSTR) is

a. 16.

b. 15.

c. 36.

d. 64.

Hide Feedback

Correct

Solution

Correct Response

a

How are treatments assigned to the experimental units in a completely randomized design?

a. The treatments are systematically assigned to the experimental units.

b. The treatments are randomly assigned to the experimental units.

c. The treatments are subjectively assigned to the experimental units.

d. Treatments are not assigned to experimental units in a completely randomized design.

Hide Feedback

Correct

Solution

Correct Response

b

The ANOVA procedure is a statistical approach for determining whether or not the means of

a. two populations are equal.

b. two samples are equal.

c. three or more populations are equal.

d. two or more samples are equal.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the following ANOVA table.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	2073.6	4
Between Blocks	6000	5	1200
Error		20	288
Total		29

The null hypothesis is to be tested at the 5% level of significance. The null hypothesis

a. should be rejected.

b. should not be tested.

c. should not be rejected.

d. should be revised.

Hide Feedback

Incorrect

Solution

Correct Response

c

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

a. 3 and 30.

b. 3 and 116.

c. 4 and 30.

d. 3 and 119.

Hide Feedback

Correct

Solution

Correct Response

b

In order to determine whether or not the means of two populations are equal,

a. either a t test or an analysis of variance can be performed.

b. an analysis of variance must be performed.

c. a t test must be performed.

d. a chi-square test can be performed.

Hide Feedback

Correct

Solution

Correct Response

a

In a completely randomized design involving three treatments, the following information is provided:

	Treatment 1	Treatment 2	Treatment 3
Sample Size	5	10	5
Sample Mean	4	8	9

The overall mean (the grand mean) for all the treatments is

a. 6.67.

b. 7.25.

c. 4.89.

d. 7.00.

Hide Feedback

Correct

Solution

Correct Response

b

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

a. 200.

b. 80.

c. 120.

d. 40.

Hide Feedback

Correct

Solution

Correct Response

d

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	180	3
Within Treatments (Error)
TOTAL	480	18

The mean square due to error (MSE) is

a. 60.

b. 15.

c. 20.

d. 18.

Hide Feedback

Correct

Solution

Correct Response

c

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	1
4	2
3	3
2	4
1	5

The least squares estimate of the intercept or b0 equals

a. -5.

b. 1.

c. 6.

d. -1.

Hide Feedback

Correct

Solution

Correct Response

c

The following information regarding a dependent variable y and an independent variable x is provided:

Σx = 90	Σ(y - ȳ)(x - x̄) = -156
Σy = 340	Σ(x - x̄)2 = 234
n = 4	Σ(y - ȳ)2 = 1974
SSR = 104

The sum of squares due to error (SSE) is

a. 234.

b. 1974.

c. 1870.

d. -156.

Hide Feedback

Correct

Solution

Correct Response

c

• Check My Work

Icon Key

The model developed from sample data that has the form of Ŷ = b0 + b1x is known as the

a. correlation model.

b. regression model.

c. estimated regression equation.

d. regression equation.

Hide Feedback

Correct

Solution

Correct Response

c

If a data set produces SST = 2000 and SSE = 800, then the coefficient of determination is

a. .4.

b. .8.

c. .5.

d. .6.

Hide Feedback

Correct

Solution

Correct Response

d

A descriptive measure of the strength of linear association between two variables is the

a. coefficient of determination.

b. standard error of the estimate.

c. correlation coefficient.

d. slope b1 of the estimated regression line.

Hide Feedback

Correct

Solution

Correct Response

c

The following information regarding a dependent variable y and an independent variable x is provided:

Σx = 90	Σ(y - ȳ)(x - x̄) = -156
Σy = 340	Σ(x - x̄)2 = 234
n = 4	Σ(y - ȳ)2 = 1974
SSR = 104

The coefficient of correlation is

a. -.0572.

b. -.2295.

c. .2295.

d. .0572.

Hide Feedback

Correct

Solution

Correct Response

b

The standard error of the estimate is the

a. square root of MSE.

b. square root of SST.

c. standard deviation of t.

d. square root of SSE.

Hide Feedback

Incorrect

Solution

Correct Response

a

If the coefficient of determination is a positive value, then the coefficient of correlation

a. must be zero.

b. can be either positive or negative.

c. can be larger than 1.

d. must also be positive.

Hide Feedback

Correct

Solution

Correct Response

b

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

a. confidence interval estimate.

b. coefficient of determination.

c. correlation coefficient.

d. standard error of the estimate.

Hide Feedback

Correct

Solution

Correct Response

b

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is the

a. residual.

b. variance.

c. prediction interval.

d. standard error.

Hide Feedback

Correct

Solution

Correct Response

a

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
12	4
3	6
7	2
6	4

The sample correlation coefficient equals

a. -.4364.

b. -.1905.

c. .1905.

d. .4364.

Hide Feedback

Correct

Solution

Correct Response

a

The following information regarding a dependent variable (y) and an independent variable (x) is provided.

y	x
4	2
3	1
4	4
6	3
8	5

SSE = 6
SST = 16

The coefficient of correlation is

a. -.7906.

b. .375.

c. .625.

d. .7906.

Hide Feedback

Incorrect

Solution

Correct Response

d

The standard error of the estimate is the

a. square root of MSE.

b. standard deviation of t.

c. square root of SST.

d. square root of SSE.

Hide Feedback

Correct

Solution

Correct Response

a

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	4
7	6
9	2
11	4

The least squares estimate of the slope or b1 equals

a. .5.

b. -10.

c. 10.

d. -.5.

Hide Feedback

Correct

Solution

Correct Response

d

The following information regarding a dependent variable y and an independent variable x is provided:

Σx = 90	Σ(y - ȳ)(x - x̄) = -156
Σy = 340	Σ(x - x̄)2 = 234
n = 4	Σ(y - ȳ)2 = 1974
SSR = 104

The sum of squares due to error (SSE) is

a. -156.

b. 1974.

c. 234.

d. 1870.

Hide Feedback

Correct

Solution

Correct Response

d

The value of the coefficient of correlation (r)

a. can be equal to the value of the coefficient of determination (r2).

b. is always smaller than the value of the coefficient of determination (r2).

c. is always larger than the value of the coefficient of determination (r2).

d. can never be equal to the value of the coefficient of determination (r2).

Hide Feedback

Correct

Solution

Correct Response

a

In regression analysis, the model in the form y = β0 + β1x + ε is called the

a. regression model.

b. correlation model.

c. estimated regression equation.

d. regression equation.

Hide Feedback

Correct

Solution

Correct Response

a

If the coefficient of determination is .90, the percentage of variation in the dependent variable explained by the variation in the independent variable is

a. .90%.

b. 81%.

c. 90%.

d. .81%.

Hide Feedback

Incorrect

Solution

Correct Response

c

Which of the following types of relationships between a dependent variable y and an independent variable x is represented by a population regression line that resembles a horizontal line?

a. A normal relationship between the mean value of y and x

b. A positive linear relationship between the mean value of y and x

c. No linear relationship between the mean value of y and x

d. A negative linear relationship between the mean value of y and x

Hide Feedback

Correct

Solution

Correct Response

c

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.

Ŷ = 500 + 4x

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

a. $900.

b. $505,000.

c. $40,500.

d. $900,000.

Hide Feedback

Correct

Solution

Correct Response

d

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	180	3
Within Treatments (Error)
TOTAL	480	18

The mean square due to treatments (MSTR) is

a. 15.

b. 18.

c. 20.

d. 60.

Hide Feedback

Correct

Solution

Correct Response

d

Which of the following is not a required assumption for the analysis of variance?

a. The variance associated with the random variable must be the same for all populations.

b. At least 2 populations are under consideration.

c. Populations under consideration have equal means.

d. The random variable of interest for each population has a normal probability distribution.

Hide Feedback

Incorrect

Solution

Correct Response

c

In order to determine whether or not the means of two populations are equal,

a. a t test must be performed.

b. either a t test or an analysis of variance can be performed.

c. a chi-square test can be performed.

d. an analysis of variance must be performed.

Hide Feedback

Correct

Solution

Correct Response

b

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The mean square due to error (MSE) is

a. 200.

b. 600.

c. 50.

d. 10.

Hide Feedback

Incorrect

Solution

Correct Response

d

A roofing company would like to implement a new method for giving estimates. The owner has narrowed his choice to three different methods. Since estimator variability is believed to be a significant factor in the overall cost estimate, each of the company's three job estimators is asked to give a cost estimate for a new roof using each of the three methods. The data will be analyzed using a randomized block design. What are the blocks in this study?

a. The estimators

b. The roofing company

c. The estimate method

d. The cost for a new roof

Hide Feedback

Correct

Solution

Correct Response

a

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The number of degrees of freedom corresponding to between-treatments is

a. 2.

b. 3.

c. 18.

d. 4.

Hide Feedback

Correct

Solution

Correct Response

d

An experimental design that permits simultaneous statistical conclusions about two or more factors is a

a. completely randomized design.

b. multiple block design.

c. randomized block design.

d. factorial design.

Hide Feedback

Correct

Solution

Correct Response

d

If H 0 is rejected for an analysis of variance, what can we conclude?

a. We can conclude that all the population means have different values.

b. We can conclude that all the population means have the same value.

c. We can conclude that at least one of the population proportions has a different value.

d.

Hide Feedback

Correct

Solution

Correct Response

d

In a completely randomized design involving three treatments, the following information is provided:

	Treatment 1	Treatment 2	Treatment 3
Sample Size	5	10	5
Sample Mean	4	8	9

The overall mean (the grand mean) for all the treatments is

a. 7.25.

b. 6.67.

c. 4.89.

d. 7.00.

Hide Feedback

Correct

Solution

Correct Response

a

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

a. 3 and 30.

b. 3 and 119.

c. 3 and 116.

d. 4 and 30.

Hide Feedback

Correct

Solution

Correct Response

c

What is the expected value of y in a simple linear regression model?

a. 0

b.

c. ε

d. 1

Hide Feedback

Correct

Solution

Correct Response

b

If two variables, x and y, have a strong linear relationship, then

a. there may or may not be any causal relationship between x and y.

b. x causes y to happen.

c. y causes x to happen.

d. the F test is used to conclude there is a causal relationship between x and y.

Hide Feedback

Correct

Solution

Correct Response

a

In simple linear regression, r2 is the

a. squared residual.

b. correlation coefficient.

c. coefficient of determination.

d. mean square error.

Hide Feedback

Correct

Solution

Correct Response

c

In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is

a. .45.

b. .85.

c. .35.

d. .65.

Hide Feedback

Correct

Solution

Correct Response

d

In a regression analysis, the coefficient of correlation is .16. The coefficient of determination in this situation is

a. 2.56.

b. .0256.

c. .4000.

d. 4.00.

Hide Feedback

Correct

Solution

Correct Response

b

It is possible for the coefficient of determination to be

a. less than 1.

b. larger than 1.

c. less than -1.

d. equal to -1.

Hide Feedback

Correct

Solution

Correct Response

a

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as the

a. regression model.

b. correlation model.

c. regression equation.

d. estimated regression equation.

Hide Feedback

Correct

Solution

Correct Response

c

The following information regarding a dependent variable (y) and an independent variable (x) is provided.

y	x
4	2
3	1
4	4
6	3
8	5

SSE = 6
SST = 16

The least squares estimate of the slope is

a. 2.

b. 4.

c. 3.

d. 1.

Hide Feedback

Correct

Solution

Correct Response

d

In a regression analysis, the standard error of the estimate is determined to be 4. In this situation, the MSE

a. depends on the sample size.

b. is 16.

c. requires a known SSE.

d. is 2.

Hide Feedback

Correct

Solution

Correct Response

b

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data

a. is 0.

b. is 1.

c. could be any value between -1 and 1.

d. is either 1 or -1, depending upon whether the relationship is positive or negative.

Hide Feedback

Correct

Solution

Correct Response

b

Consider the following ANOVA table for a simple linear regression.

What is the value of the mean square error for this regression analysis?

a. 20.2

b. 9

c. 37.4

d. 336.5

Hide Feedback

Incorrect

Solution

Correct Response

c

The coefficient of correlation

a. is the square root of the r-square.

b. can never be equal to r-square.

c. is the square of the r-square.

d. can never be negative.

Hide Feedback

Correct

Solution

Correct Response

a

As the value of the coefficient of determination increases, the

a. absolute value of the regression equation's slope decreases.

b. total number of degrees of freedom increases.

c. value of the correlation coefficient decreases.

d. goodness of fit for the estimated regression equation increases.

Hide Feedback

Incorrect

Solution

Correct Response

d

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Σx = 90	Σ(y - ȳ)(x - x̄) = 466
Σy = 170	Σ(x - x̄)2 = 234
n = 10	Σ(y - ȳ)2 = 1434
SSE = 505.98

The least squares estimate of the intercept or b0 equals

a. .923.

b. -.923.

c. 1.991.

d. -1.991.

Hide Feedback

Incorrect

Solution

Correct Response

b

Which data point in the following scatter diagram would most likely be an influential observation?

a. A

b. F

c. D

d. None of the data points appears to be an influential observation.

Hide Feedback

Correct

Solution

Correct Response

b

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

a. 3 and 119.

b. 4 and 30.

c. 3 and 116.

d. 3 and 30.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the following information.

SSTR = 6750	H0: μ1 = μ2 = μ3 = μ4
SSE = 8000	Ha: At least one mean is different

The mean square due to treatments (MSTR) equals

a. 500.

b. 400.

c. 2250.

d. 1687.5.

Hide Feedback

Correct

Solution

Correct Response

c

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The number of degrees of freedom corresponding to within-treatments is

a. 18.

b. 22.

c. 5.

d. 4.

Hide Feedback

Correct

Solution

Correct Response

a

A roofing company would like to implement a new method for giving estimates. The owner has narrowed his choice to three different methods. Since estimator variability is believed to be a significant factor in the overall cost estimate, each of the company's three job estimators is asked to give a cost estimate for a new roof using each of the three methods. The data will be analyzed using a randomized block design. What are the blocks in this study?

a. The roofing company

b. The estimate method

c. The cost for a new roof

d. The estimators

Hide Feedback

Correct

Solution

Correct Response

d

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The test statistic is

a. .2.

b. 15.

c. 5.0.

d. 3.75.

Hide Feedback

Correct

Solution

Correct Response

c

The number of times each experimental condition is observed in a factorial design is known as

a. replication.

b. factor.

c. partition.

d. blocking.

Hide Feedback

Correct

Solution

Correct Response

a

In a completely randomized design involving three treatments, the following information is provided:

	Treatment 1	Treatment 2	Treatment 3
Sample Size	5	10	5
Sample Mean	4	8	9

The overall mean (the grand mean) for all the treatments is

a. 7.25.

b. 6.67.

c. 7.00.

d. 4.89.

Hide Feedback

Correct

Solution

Correct Response

a

Consider the following information.

SSTR = 6750	H0: μ1 = μ2 = μ3 = μ4
SSE = 8000	Ha: At least one mean is different

If n = 5, the mean square due to error (MSE) equals

a. 2250.

b. 1687.5.

c. 400.

d. 500.

Hide Feedback

Correct

Solution

Correct Response

d

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment	Observations
A	20	30	25	33
B	22	26	20	28
C	40	30	28	22

The null hypothesis for this ANOVA problem is

a. μ1 = μ2 = μ3 = μ4.

b. μ1 = μ2 = ... = μ12.

c. μ1 = μ2.

d. μ1 = μ2 = μ3.

Hide Feedback

Correct

Solution

Correct Response

d

The following information regarding a dependent variable (y) and an independent variable (x) is provided.

y	x
4	2
3	1
4	4
6	3
8	5

SSE = 6
SST = 16

The least squares estimate of the y-intercept is

a. 1.

b. 4.

c. 2.

d. 3.

Hide Feedback

Correct

Solution

Correct Response

c

A descriptive measure of the strength of linear association between two variables is the

a. coefficient of determination.

b. slope b1 of the estimated regression line.

c. standard error of the estimate.

d. correlation coefficient.

Hide Feedback

Correct

Solution

Correct Response

d

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

a. 80%.

b. .80%.

c. .64%.

d. 64%.

Hide Feedback

Incorrect

Solution

Correct Response

d

In simple linear regression analysis, which of the following is not true?

a. The value of F = t2.

b. The F test and the t test yield the same conclusion.

c.  Which of the following types of relationships between a dependent variable y and an independent variable x is represented by a population regression line that resembles a horizontal line?

d. The relationship between x and y is represented by a straight line.

Hide Feedback

Correct

Solution

Correct Response

c

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	1
4	2
3	3
2	4
1	5

The least squares estimate of the intercept or b0 equals

a. 1.

b. 6.

c. -5.

d. -1.

Hide Feedback

Correct

Solution

Correct Response

b

The model developed from sample data that has the form of Ŷ = b0 + b1x is known as the

a. regression equation.

b. regression model.

c. correlation model.

d. estimated regression equation.

Hide Feedback

Correct

Solution

Correct Response

d

Compared to the confidence interval estimate for a particular value of y in a linear regression model, the interval estimate for an average value of y will be

a. easy to determine.

b. narrower.

c. the same.

d. wider.

Hide Feedback

Correct

Solution

Correct Response

b

Following a regression analysis, an examination of graphical plots was performed to determine whether the assumptions for ε are appropriate. Consider the following plot from this analysis:

What type of plot is this?

a. A plot of the standardized residuals against values of the independent variable

b. A plot of the residuals against the predicted values of the dependent variable

c. A normal probability plot

d. A plot of the residuals against values of the dependent variable

Hide Feedback

Correct

Solution

Correct Response

c

In a regression and correlation analysis, if r2 = 1, then

a. SSE must also be equal to one.

b. SSE can be any positive value.

c. SSE must be equal to zero.

d. SSE must be negative.

Hide Feedback

Correct

Solution

Correct Response

c

In regression analysis, the model in the form y = β0 + β1x + ε is called the

a. regression model.

b. regression equation.

c. correlation model.

d. estimated regression equation.

Hide Feedback

Correct

Solution

Correct Response

a

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The number of degrees of freedom corresponding to within-treatments is

a. 5.

b. 22.

c. 18.

d. 4.

Hide Feedback

Incorrect

Solution

Correct Response

c

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment		Observations
A	20	30	25	33
B	22	26	20	28
C	40	30	28	22

The null hypothesis is to be tested at the 1% level of significance. The null hypothesis

a. should be rejected.

b. should be revised.

c. should not be tested.

d. should not be rejected.

Hide Feedback

Correct

Solution

Correct Response

d

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The critical value of F occurs with

a. 6 numerator and 20 denominator degrees of freedom.

b. 5 numerator and 20 denominator degrees of freedom.

c. 5 numerator and 114 denominator degrees of freedom.

d. 6 numerator and 114 denominator degrees of freedom.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the following ANOVA table.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	2073.6	4
Between Blocks	6000	5	1200
Error		20	288
Total		29

The sum of squares due to error equals

a. 2073.6.

b. 6000.

c. 5760.

d. 13833.6.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the following ANOVA table.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	2073.6	4
Between Blocks	6000	5	1200
Error		20	288
Total		29

The null hypothesis is to be tested at the 5% level of significance. The p-value is

a. greater than .10.

b. between .05 to .10.

c. between .025 to .05.

d. less than .01.

Hide Feedback

Correct

Solution

Correct Response

a

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The number of degrees of freedom corresponding to between-treatments is

a. 18.

b. 4.

c. 3.

d. 2.

Hide Feedback

Correct

Solution

Correct Response

b

If H 0 is rejected for an analysis of variance, what can we conclude?

a. We can conclude that all the population means have different values.

b. We can conclude that all the population means have the same value.

c. We can conclude that at least one of the population means has a different value than the other population means.

d. We can conclude that at least one of the population proportions has a different value.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the following information.

SSTR = 6750	H0: μ1 = μ2 = μ3 = μ4
SSE = 8000	Ha: At least one mean is different

The test statistic to test the null hypothesis equals

a. .84.

b. 4.22.

c. .22.

d. 4.50.

Hide Feedback

Correct

Solution

Correct Response

d

The mean square is the sum of squares divided by

a. its corresponding degrees of freedom.

b. its corresponding degrees of freedom minus one.

c. the total number of replications.

d. the total number of observations.

Hide Feedback

Correct

Solution

Correct Response

a

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

The mean square due to treatments (MSTR) is

a. 36.

b. 64.

c. 15.

d. 16.

Hide Feedback

Correct

Solution

Correct Response

d

Following a regression analysis, an examination of graphical plots was performed to determine whether the assumptions for ε are appropriate. Consider the following plot from this analysis:

What type of plot is this?

a. A plot of the residuals against the predicted values of the dependent variable

b. A plot of the residuals against values of the dependent variable

c. A normal probability plot

d. A plot of the standardized residuals against values of the independent variable

Hide Feedback

Correct

Solution

Correct Response

c

In regression analysis, if the independent variable is measured in pounds, the dependent variable

a. must also be in pounds.

b. can be measured in any units.

c. must be in some unit of weight.

d. cannot be in pounds.

Hide Feedback

Correct

Solution

Correct Response

b

The coefficient of correlation

a. can never be equal to r-square.

b. can never be negative.

c. is the square root of the r-square.

d. is the square of the r-square.

Hide Feedback

Correct

Solution

Correct Response

c

If the coefficient of correlation is .90, then the coefficient of determination

a. is also .90.

b. will be -.90.

c. is either .81 or -.81.

d. must be .81.

Hide Feedback

Correct

Solution

Correct Response

d

In a regression analysis, the coefficient of correlation is .16. The coefficient of determination in this situation is

a. .0256.

b. .4000.

c. 2.56.

d. 4.00.

Hide Feedback

Correct

Solution

Correct Response

a

Which of the following sum of squares statements is correct for a regression analysis?

a. SSR = SSE + SST

b. SST = SSR + SSE

c. SST = SSR – SSE

d. SSE = SSR + SST

Hide Feedback

Correct

Solution

Correct Response

b

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
12	4
3	6
7	2
6	4

The coefficient of determination equals

a. .4364.

b. .1905.

c. -.4364.

d. -.1905.

Hide Feedback

Correct

Solution

Correct Response

b

In a regression analysis, if SST = 500 and SSE = 300, then the coefficient of determination is

a. .40.

b. .60.

c. .67.

d. .20.

Hide Feedback

Correct

Solution

Correct Response

a

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Σx = 90	Σ(y - ȳ)(x - x̄) = 466
Σy = 170	Σ(x - x̄)2 = 234
n = 10	Σ(y - ȳ)2 = 1434
SSE = 505.98

The least squares estimate of the intercept or b0 equals

a. -1.991.

b. .923.

c. -.923.

d. 1.991.

Hide Feedback

Correct

Solution

Correct Response

c

If only MSE is known, you can compute the

a. coefficient of correlation.

b. ith residual.

c. r-square.

d. standard error.

Hide Feedback

Correct

Solution

Correct Response

d

Which of the following statements is true for a randomized block design when comparing treatment effects?

a. The null hypothesis is that the block means are equal.

b. The test statistic is F = MSTR/MSE.

c. The null hypothesis is that at least two of the block means differ.

d. The test statistic is F = MSB/MSE.

Hide Feedback

Correct

Solution

Correct Response

b

An experimental design where the experimental units are randomly assigned to the treatments is known as a

a. factor block design.

b. random factor design.

c. completely randomized design.

d. None of these choices.

Hide Feedback

Correct

Solution

Correct Response

c

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is

a. 14.8.

b. 13.32.

c. 133.2.

d. 30.0.

Hide Feedback

Correct

Solution

Correct Response

a

What does the analysis of variance procedure compare to determine whether the population means are equal?

a. The population variances and the sample variances

b. The population means

c. The sample proportions

d. The between-treatments estimate of σ 2 and the within-treatments estimate of σ 2

Hide Feedback

Correct

Solution

Correct Response

d

In an ANOVA procedure, a term that means the same as the term "variable" is

a. treatment.

b. replication.

c. within-variance.

d. factor.

Hide Feedback

Correct

Solution

Correct Response

d

The process of using the same or similar experimental units for all treatments is called

a. blocking.

b. replicating.

c. partitioning.

d. factoring.

Hide Feedback

Correct

Solution

Correct Response

a

Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained.

Ŷ = 120 - 10x

Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

a. increase by 20 units.

b. decease by 20 units.

c. increase by 120 units.

d. decrease by 100 units.

Hide Feedback

Correct

Solution

Correct Response

b

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	4
7	6
9	2
11	4

The least squares estimate of the intercept or b0 equals

a. 10.

b. -.5.

c. -10.

d. .5.

Hide Feedback

Correct

Solution

Correct Response

a

In regression analysis, the error term ε is a random variable with a mean or expected value of

a. 1.

b. x̄.

c. 0.

d. μ.

Hide Feedback

Correct

Solution

Correct Response

c

For the following data, the value of SSE = 18.

Dependent Variable (y)	Independent Variable (x)
15	4
17	6
23	2
17	4

The coefficient of determination (r2) equals

a. .5.

b. -.5.

c. .7071.

d. -.7071.

Hide Feedback

Correct

Solution

Correct Response

a

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
12	4
3	6
7	2
6	4

The least squares estimate of the slope or b1 equals

a. -1.

b. 1.

c. 11.

d. -11.

Hide Feedback

Correct

Solution

Correct Response

a

In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then

a. the estimated regression line intercepts the positive y-axis.

b. if x is increased, y must also increase.

c. if y is increased, x must also increase.

d. there is a positive correlation between x and y.

Hide Feedback

Correct

Solution

Correct Response

a

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation:

Ŷ = 9 - 3x

The above equation implies that if the price is increased by $1, the demand is expected to

a. increase by 6 units.

b. decrease by 3 units.

c. decrease by 3000 units.

d. decrease by 6000 units.

Hide Feedback

Correct

Solution

Correct Response

c

In a regression analysis, if SSE = 500 and SSR = 300, then the coefficient of determination is

a. .625.

b. .375.

c. .167.

d. .600.

Hide Feedback

Correct

Solution

Correct Response

b

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The sum of squares due to error (SSE) is

a. 1000.

b. 1600.

c. 200.

d. 600.

Hide Feedback

Correct

Solution

Correct Response

d

In the ANOVA, treatments refer to

a. experimental units.

b. different levels of a factor.

c. the dependent variables.

d. statistical applications.

Hide Feedback

Correct

Solution

Correct Response

b

How many degrees of freedom will the error have in a randomized block design with five treatments and three blocks?

a. 2

b. 8

c. 4

d. It will depend on the total sample size.

Hide Feedback

Correct

Solution

Correct Response

b

The process of allocating the total sum of squares and degrees of freedom to the various components is called

a. blocking.

b. factoring.

c. replicating.

d. partitioning.

Hide Feedback

Correct

Solution

Correct Response

d

A major retail chain with 100 stores across the country is interested in the effects of advertising on local television stations. A random sample of 18 stores is selected. The retailer has made three different commercials, each of which is randomly assigned to six stores. The total sales for the month following the airing of the commercials are recorded. How many replicates have been used in this completely randomized design?

a. 18

b. 3

c. 10

d. 6

Hide Feedback

Correct

Solution

Correct Response

d

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment		Observations
A	20	30	25	33
B	22	26	20	28
C	40	30	28	22

The null hypothesis is to be tested at the 1% level of significance. The p-value is

a. between .01 to .025.

b. greater than .1.

c. between .05 to .10.

d. less than .01.

Hide Feedback

Correct

Solution

Correct Response

b

Which of the following describes the relationship between a confidence interval for y at a given value of x and a prediction interval for y at the same value of x?

a. The confidence interval will be the same width as the prediction interval.

b. The confidence interval will always be half the width of the prediction interval.

c. The confidence interval will be wider than the prediction interval.

d. The confidence interval will be narrower than the prediction interval.

Hide Feedback

Correct

Solution

Correct Response

d

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

Ŷ = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = .2683

The F statistic computed from the above data is

a. 50.

b. 48.

c. 3.

d. 45.

Hide Feedback

Correct

Solution

Correct Response

d

In regression analysis, if the independent variable is measured in pounds, the dependent variable

a. can be measured in any units.

b. must also be in pounds.

c. must be in some unit of weight.

d. cannot be in pounds.

Hide Feedback

Correct

Solution

Correct Response

a

For the following data, the value of SSE = 18.

Dependent Variable (y)	Independent Variable (x)
15	4
17	6
23	2
17	4

The total sum of squares (SST) equals

a. 9.

b. 36.

c. 18.

d. 2.

Hide Feedback

Correct

Solution

Correct Response

b

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained.

Ŷ = 50 + 8x

Based on the above estimated regression line, if advertising is $1000, then the point estimate for sales (in dollars) is

a. $8050.

b. $130.

c. $130,000.

d. $1,300,000.

Hide Feedback

Correct

Solution

Correct Response

d

Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation was obtained.

Ŷ = 80 + 6.2x

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

a. $142,000.

b. $62,080.

c. $700,000.

d. $700.

Hide Feedback

Correct

Solution

Correct Response

c

In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is

a. .1785.

b. .4225.

c. .65 if b1 is positive.

d. -.18 if b1 is negative.

Hide Feedback

Correct

Solution

Correct Response

c

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see a

a. widening band of points around the x-axis.

b. band of points having a slope consistent with that of the regression equation.

c. horizontal band of points centered near zero.

d. parabolic band of points centered at the origin.

Hide Feedback

Correct

Solution

Correct Response

c

The interval estimate of the mean value of y for a given value of x is the

a. x versus y correlation interval.

b. confidence interval estimate.

c. average regression interval.

d. prediction interval estimate.

Hide Feedback

Correct

Solution

Correct Response

b

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	4
7	6
9	2
11	4

The sample correlation coefficient equals

a. .3162.

b. .10.

c. -.10.

d. -.3162.

Hide Feedback

Incorrect

Solution

Correct Response

d

The Minitab output for a regression analysis relating the temperature in a warehouse to the machine settings within the warehouse is given below.

What is the t test statistic used to determine whether the setting is related to the temperature?

a. t = 1.38734

b. t = 16.79

c. t = 5887.95

d. t = 76.73

Hide Feedback

Correct

Solution

Correct Response

d

In simple linear regression, r2 is the

a. squared residual.

b. coefficient of determination.

c. mean square error.

d. correlation coefficient.

Hide Feedback

Correct

Solution

Correct Response

b

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the

a. observed values of the independent variable and the predicted values of the independent variable.

b. observed values of the dependent variable and the predicted values of the independent variable.

c.  In simple linear regression analysis, which of the following is not true? In simple linear regression analysis, which of the following is not true?

d. observed values of the independent variable and the predicted values of the dependent variable.

Hide Feedback

Correct

Solution

Correct Response

c

In a regression analysis, if SSE = 500 and SSR = 300, then the coefficient of determination is

a. .625.

b. .600.

c. .375.

d. .167.

Hide Feedback

Correct

Solution

Correct Response

c

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

Ŷ = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = .2683

To perform an F test, the p-value is

a. between .025 and .05.

b. greater than .10.

c. between .01 and .025.

d. less than .01.

Hide Feedback

Correct

Solution

Correct Response

d

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

The number of degrees of freedom corresponding to within-treatments is

a. 60.

b. 5.

c. 59.

d. 4.

Hide Feedback

Incorrect

Solution

Correct Response

a

If H 0 is rejected for an analysis of variance, what can we conclude?

a. We can conclude that at least one of the population means has a different value than the other population means.

b. We can conclude that at least one of the population proportions has a different value.

c. We can conclude that all the population means have the same value.

d. We can conclude that all the population means have different values.

Hide Feedback

Correct

Solution

Correct Response

a

In the analysis of variance procedure (ANOVA), "factor" refers to

a. different levels of a treatment.

b. the independent variable.

c. the dependent variable.

d. the critical value of F.

Hide Feedback

Correct

Solution

Correct Response

b

Consider the following information.

SSTR = 6750	H0: μ1 = μ2 = μ3 = μ4
SSE = 8000	Ha: At least one mean is different

The test statistic to test the null hypothesis equals

a. .84.

b. 4.22.

c. .22.

d. 4.50.

Hide Feedback

Correct

Solution

Correct Response

d

Consider the following information.

SSTR = 6750	H0: μ1 = μ2 = μ3 = μ4
SSE = 8000	Ha: At least one mean is different

The null hypothesis is to be tested at the 5% level of significance. The null hypothesis

a. was designed incorrectly.

b. should be rejected.

c. should not be rejected.

d. cannot be tested.

Hide Feedback

Correct

Solution

Correct Response

b

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Treatment		Observations
A	20	30	25	33
B	22	26	20	28
C	40	30	28	22

The test statistic to test the null hypothesis equals

a. 3.13.

b. .944.

c. 19.231.

d. 1.06.

Hide Feedback

Correct

Solution

Correct Response

d

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.

SSTR = 200 (Sum of Squares Due to Treatments)

SST = 800 (Total Sum of Squares)

If, at a 5% level of significance, we want to determine whether or not the means of the five populations are equal, the critical value of F is

a. 4.98.

b. 19.48.

c. 5.69.

d. 2.53.

Hide Feedback

Correct

Solution

Correct Response

d

Consider the following ANOVA table.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	2073.6	4
Between Blocks	6000	5	1200
Error		20	288
Total		29

The test statistic to test the null hypothesis equals

a. 1.8.

b. .432.

c. 28.8.

d. 4.17.

Hide Feedback

Correct

Solution

Correct Response

a

In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the

a. sum of observations.

b. population means.

c. overall sample mean.

d. means of each sample.

Hide Feedback

Correct

Solution

Correct Response

c

A high leverage point is an observation that has an extreme value for which of the following?

a. The mean

b. The dependent variable

c. The independent variable

d. The residual

Hide Feedback

Correct

Solution

Correct Response

c

In testing for the equality of k population means, the number of treatments is

a. k - 1.

b. nT.

c. nT - k.

d. k.

Hide Feedback

Incorrect

Solution

Correct Response

d

A manager is considering three new machines for filling boxes of cereal at a processing plant. Each of the three machines is assigned to 10 randomly selected employees. The time required to fill 25 boxes using the machine is recorded. How many treatments does this single-factor experiment have?

a. 1

b. 25

c. 10

d. 3

Hide Feedback

Correct

Solution

Correct Response

d

Consider the following ANOVA table.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	2073.6	4
Between Blocks	6000	5	1200
Error		20	288
Total		29

The mean square due to treatments equals

a. 288.

b. 8294.4.

c. 518.4.

d. 1200.

Hide Feedback

Correct

Solution

Correct Response

c

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

Ŷ = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = .2683


Based on the above estimated regression equation, if advertising is $3000, then the point estimate for sales (in dollars) is

a. $66.

b. $5412.

c. $17,400.

d. $66,000.

Hide Feedback

Correct

Solution

Correct Response

d

The following information regarding a dependent variable (y) and an independent variable (x) is provided.

y	x
4	2
3	1
4	4
6	3
8	5

SSE = 6
SST = 16

The MSE is

a. 2.

b. 4.

c. 3.

d. 1.

Hide Feedback

Correct

Solution

Correct Response

a

If the coefficient of determination is equal to 1, then the coefficient of correlation

a. must also be +1.

b. can be any value between -1 to +1.

c. must be -1.

d. can be either -1 or +1.

Hide Feedback

Correct

Solution

Correct Response

d

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation:

Ŷ = 30,000 + 4x

The above equation implies that an

a. increase of $1 in advertising is associated with an increase of $4 in sales.

b. increase of $1 in advertising is associated with an increase of $34,000 in sales.

c. increase of $4 in advertising is associated with an increase of $4000 in sales.

d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Hide Feedback

Correct

Solution

Correct Response

d

If there is a very weak correlation between two variables, then the coefficient of determination must be

a. equal to one.

b. much smaller than -1, if the correlation is negative.

c. much larger than 1, if the correlation is positive.

d. closer or equal to zero.

Hide Feedback

Incorrect

Solution

Correct Response

d

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

a. estimation analysis.

b. the regression model.

c. correlation analysis.

d. the correlation model.

Hide Feedback

Correct

Solution

Correct Response

b

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see a

a. widening band of points around the x-axis.

b. band of points having a slope consistent with that of the regression equation.

c. horizontal band of points centered near zero.

d. parabolic band of points centered at the origin.

Hide Feedback

Correct

Solution

Correct Response

c

The interval estimate of the mean value of y for a given value of x is the

a. x versus y correlation interval.

b. confidence interval estimate.

c. average regression interval.

d. prediction interval estimate.

Hide Feedback

Correct

Solution

Correct Response

b

You are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	4
7	6
9	2
11	4

The sample correlation coefficient equals

a. .3162.

b. .10.

c. -.10.

d. -.3162.

Hide Feedback

Incorrect

Solution

Correct Response

d

The Minitab output for a regression analysis relating the temperature in a warehouse to the machine settings within the warehouse is given below.

What is the t test statistic used to determine whether the setting is related to the temperature?

a. t = 1.38734

b. t = 16.79

c. t = 5887.95

d. t = 76.73

Hide Feedback

Correct

Solution

Correct Response

d

In simple linear regression, r2 is the

a. squared residual.

b. coefficient of determination.

c. mean square error.

d. correlation coefficient.

Hide Feedback

Correct

Solution

Correct Response

b

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the

a. observed values of the independent variable and the predicted values of the independent variable.

b. observed values of the dependent variable and the predicted values of the independent variable.

c. observed values of the dependent variable and the predicted values of the dependent variable.

d. observed values of the independent variable and the predicted values of the dependent variable.

Hide Feedback

Correct

Solution

Correct Response

c

In a regression analysis, if SSE = 500 and SSR = 300, then the coefficient of determination is

a. .625.

b. .600.

c. .375.

d. .167.

Hide Feedback

Correct

Solution

Correct Response

c

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

Ŷ = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = .2683

To perform an F test, the p-value is

a. between .025 and .05.

b. greater than .10.

c. between .01 and .025.

d. less than .01.

Hide Feedback

Correct

Solution

Correct Response

d

f a data set produces SST = 2000 and SSE = 800, then the coefficient of determination is

a. .6.

b. .4.

c. .5.

d. .8.

Hide Feedback

Correct

Solution

Correct Response

a

The coefficient of correlation

a. is the square of the r-square.

b. is the square root of the r-square.

c. can never be equal to r-square.

d. can never be negative.

Hide Feedback

Correct

Solution

Correct Response

b

The interval estimate of the mean value of y for a given value of x is the

a. confidence interval estimate.

b. average regression interval.

c. prediction interval estimate.

d. x versus y correlation interval.

Hide Feedback

Correct

Solution

Correct Response

a

In regression analysis, which of the following assumptions is not true about the error term ε?

a. The error term is normally distributed.

b. The expected value of the error term is one.

c. The values of the error term are independent.

d. The variance of the error term is the same for all values of x.

Hide Feedback

Correct

Solution

Correct Response

b

The value of the coefficient of correlation (r)

a. is always smaller than the value of the coefficient of determination (r2).

b. is always larger than the value of the coefficient of determination (r2).

c. can never be equal to the value of the coefficient of determination (r2).

d. can be equal to the value of the coefficient of determination (r2).

Hide Feedback

Correct

Solution

Correct Response

d

In the following estimated regression equation Ŷ = b0 + b1x,

a. b1 is the slope.

b. b1x is the intercept.

c. b1x is the slope.

d. b1 is the intercept.

Hide Feedback

Correct

Solution

Correct Response

a

If the coefficient of determination is a positive value, then the coefficient of correlation

a. must be zero.

b. can be larger than 1.

c. must also be positive.

d. can be either positive or negative.

Hide Feedback

Correct

Solution

Correct Response

d

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained.

Ŷ = 50 + 8x

Based on the above estimated regression line, if advertising is $1000, then the point estimate for sales (in dollars) is

a. $130,000.

b. $8050.

c. $1,300,000.

d. $130.

Hide Feedback

Correct

Solution

Correct Response

c

Consider the Minitab output from a regression analysis relating the length of a rod to its weight. Interval estimates were also obtained for a rod of length 2.5 inches.

Which of the following represents the estimated regression equation?

a.

b.

c.

d.

Hide Feedback

Correct

Solution

Correct Response

c

SSE can never be

a. smaller than SST.

b. equal to one.

c. equal to zero.

d. larger than SST.

Hide Feedback

Correct

Solution

Correct Response

d

Consider the following scatter diagram.

Which of the following could be the value of the sample correlation coefficient for this scatter diagram?

a. rxy = –.87

b. rxy = –1

c. rxy = .25

d. rxy = .90

Hide Feedback

Correct

Solution

Correct Response

a

In a regression and correlation analysis, if r2 = 1, then

a. SSE can be any positive value.

b. SSE must also be equal to one.

c. SSE must be equal to zero.

d. SSE must be negative.

Hide Feedback

Correct

Solution

Correct Response

c

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained.

Ŷ = 12 + 1.8x

n = 17
SSR = 225
SSE = 75
sb1 = .2683

The t statistic for testing the significance of the slope is

a. 1.80.

b. 6.71.

c. 1.96.

d. .56.

Hide Feedback

Correct

Solution

Correct Response

b

What is the expected value of y in a simple linear regression model?

a. 0

b. ε

c.

d. 1

Hide Feedback

Correct

Solution

Correct Response

c

In regression analysis, the independent variable is

a. used to predict other independent variables.

b. used to predict the dependent variable.

c. the variable that is being predicted.

d. the variable that is not used for prediction.

Hide Feedback

Correct

Solution

Correct Response

b

ou are given the following information about y and x.

Dependent Variable (y)	Independent Variable (x)
5	1
4	2
3	3
2	4
1	5

The least squares estimate of the slope or b1 equals

a. 6.

b. -1.

c. 1.

d. -5.

Hide Feedback

Correct

Solution

Correct Response

b

A high leverage point is an observation that has an extreme value for which of the following?

a. The dependent variable

b. The residual

c. The independent variable

d. The mean

Hide Feedback

Correct

Solution

Correct Response

c

It is possible for the coefficient of determination to be

a. equal to -1.

b. less than -1.

c. larger than 1.

d. less than 1.

Hide Feedback

Correct

Solution

Correct Response

d

In the following estimated regression equation Ŷ = b0 + b1x,

a. b1x is the slope.

b. b1 is the slope.

c. b1 is the intercept.

d. b1x is the intercept.

Hide Feedback

Correct

Solution

Correct Response

b

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Σx = 90	Σ(y - ȳ)(x - x̄) = 466
Σy = 170	Σ(x - x̄)2 = 234
n = 10	Σ(y - ȳ)2 = 1434
SSE = 505.98

The sample correlation coefficient equals

a. .3528.

b. -.8045.

c. -.3528.

d. .8045.

Hide Feedback

Correct

Solution

Correct Response

d

The following information regarding a dependent variable y and an independent variable x is provided:

Σx = 90	Σ(y - ȳ)(x - x̄) = -156
Σy = 340	Σ(x - x̄)2 = 234
n = 4	Σ(y - ȳ)2 = 1974
SSR = 104

The slope of the regression equation is

a. .667.

b. -.667.

c. 100.

d. -100.

Hide Feedback

Correct

Solution

Correct Response

b

A least squares regression line

a. implies a cause-and-effect relationship between x and y.

b. ensures that the predictions of y outside the range of the values of x are valid.

c. can be used to predict a value of y if the corresponding x value is given.

d. can only be determined if a good linear relationship exists between x and y.

Hide Feedback

Correct

Solution

Correct Response

c