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Given
are five observations collected in a regression study on two variables.
a. Which of the following scatter diagrams accurately represents
the data?
b. Develop the estimated regression equation for these data
(to decimal). c. Use the estimated regression equation to predict the value
of when (to decimal).
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Brawdy
Plastics, Inc., produces plastic seat belt retainers for General Motors at their
plant in Buffalo, New York. After final assembly and painting, the parts are
placed on a conveyor belt that moves the parts past a final inspection
station. How fast the parts move past the final inspection station depends
upon the line speed of the conveyor belt (feet per minute). Although faster
line speeds are desirable, management is concerned that increasing the line
speed too much may not provide enough time for inspectors to identify which
parts are actually defective. To test this theory, Brawdy Plastics conducted
an experiment in which the same batch of parts, with a known number of
defective parts, was inspected using a variety of line speeds. The following
data were collected.
If
required, enter negative values as negative numbers. a. Select a scatter diagram with the line speed as the independent
variable.
b. What does the scatter diagram developed in part (a) indicate about the
relationship between the two variables? c. Use the least squares method to develop the estimated regression
equation (to 1 decimal). d. Predict the number of defective parts found for a line speed
of feet per minute.
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David's
Landscaping has collected data on home values (in thousands of $) and
expenditures (in thousands of $) on landscaping with the hope of developing a
predictive model to help marketing to potential new clients. Data
for households may be found in the file Landscape.
Click on the datafile logo to reference the data.
If
required, enter negative values as negative numbers. a. Select a scatter diagram with home value as the independent variable.
b. What does the scatter plot developed in part (a) indicate about the relationship
between the two variables? The
scatter diagram indicates a linear
relationship between the two variables. c. Use the least squares method to develop the estimated regression
equation (to decimals). + d. For every additional in home value, estimate how much
additional will be spent on landscaping (to decimals). $ e. Use the equation estimated in part (c) to predict the landscaping
expenditures for a home valued at (to the nearest whole number). $
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A
large city hospital conducted a study to investigate the relationship between
the number of unauthorized days that employees are absent per year and the
distance (miles) between home and work for the employees. A sample
of employees was selected and the following data were collected.
If
required, enter negative values as negative numbers. a. Select the correct scatter diagram for these data.
Does
a linear relationship appear reasonable? b. Develop the least squares estimated regression equation that relates
the distance to work to the number of days absent (to decimals). c. Predict the number of days absent for an employee that lives miles
from the hospital (to nearest whole number). days
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Given
are five observations for two variables, and . Excel
File: data14-17.xlsx The
estimated regression equation for these data is . Compute
SSE, SST, and SSR (to decimal).
What
percentage of the total sum of squares can be accounted for by the estimated
regression equation (to decimal)? What
is the value of the sample correlation coefficient (to decimals)?
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An
important application of regression analysis in accounting is in the
estimation of cost. By collecting data on volume and cost and using the least
squares method to develop an estimated regression equation relating volume
and cost, an accountant can estimate the cost associated with a particular
manufacturing volume. Consider the following sample of production volumes and
total cost data for a manufacturing operation.
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Given
are five observations for two variables, and . Excel
File: data14-25.xlsx The
estimated regression equation is . a. What is the value of the standard error of the estimate
(to decimals)? b. Test for a significant relationship by using the t test.
Use . What
is the -value? Use Table 2 of Appendix B. . What
is your conclusion ()? c. Use the test to test for a significant relationship.
Use . Compute
the value of the test statistic (to decimals). What
is the -value? Use Table 4 of Appendix B. What
is your conclusion?
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Consider
the following data on production volume and total
cost for a particular manufacturing operation.
The
estimated regression equation is . Use to
test whether the production volume is significantly related to the total
cost. Complete
the ANOVA table. Enter all values with nearest whole number, except
the test statistic (to decimals) and the -value
(to decimals).
What
is your conclusion?
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Consider
the data set below. Use Table 2 of Appendix B. Excel
File: data14-33.xlsx a. Estimate the standard deviation
of when (to decimals). b. Develop a confidence interval for the expected value of when (to decimals). ( , ) c.Estimate the standard deviation of an individual value
of when (to decimals). d. Develop a prediction interval
for when (to decimals). ( , )
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Data
given below are on the adjusted gross income and the amount of
itemized deductions taken by taxpayers. Data were reported in thousands of
dollars. With the estimated regression equation , the point estimate of
a reasonable level of total itemized deductions for a taxpayer with an
adjusted gross income of is . Click on the datafile to
reference the data. Excel
File: data14-37.xlsx
Use
the estimated regression coefficients rounded to decimals in your
calculations. а. Develop a confidence interval for the mean amount of
total itemized deductions for all taxpayers with an adjusted gross income
of (to decimals). $ thousand to $ thousand b. Develop a prediction interval estimate for the amount
of total itemized deductions for a particular taxpayer with an adjusted gross
income of (to decimals). $ thousand to $ thousand c. If the particular taxpayer referred to in part (b) claimed total
itemized deductions of , would the IRS agent's request for an audit appear
to be justified? ,
it is than
anticipated. d. Use your answer to part (b) to give the IRS agent a guideline as
to the amount of total itemized deductions a taxpayer with an adjusted gross
income of should claim before an audit is recommended (to the
nearest whole number). Any
deductions exceeding the $ upper limit could suggest an audit.
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The
Wall Street Journal asked Concur Technologies,
Inc., an expense management company, to examine data from million
expense reports to provide insights regarding business travel expenses. Their
analysis of the data showed that New York was the most expensive city. The
following table shows the average daily hotel room rate () and the average amount
spent on entertainment () for a random sample of of
the most-visited U.S. cities. These data lead to the estimated
regression equation . For these data . Click on the datafile logo
to reference the data. Use Table 1 of Appendix B.
a. Predict the amount spent on entertainment for a particular city that
has a daily room rate of (to decimals). b. Develop a confidence interval for the mean amount spent on entertainment
for all cities that have a daily room rate
of (to decimals). c. The average room rate in Chicago is . Develop
a prediction interval for the amount spent on entertainment in
Chicago (to decimals).
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Following
is a portion of the regression output for an application relating maintenance
expense (dollars per month) to usage (hours per week) for a particular brand
of computer terminal. Excel
File: data14-41.xlsx
If
your answer is zero, enter "". a. Write the estimated regression equation (to decimals). + b. Use a test to determine whether monthly maintenance expense
is related to usage at the level of significance
(to decimals). Use Table 2 of Appendix B.
the
null hypothesis. Monthly maintenance expense related
to usage. c. Did the estimated regression equation provide a good fit? Explain.
Hint: If is greater than , the estimated regression equation
provides a good fit. ,
because the value of is than .
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Given
are the data for two variables, and . Do not round your
intermediate calculations.
a. Develop an estimated regression equation for these data by computing and (to decimals).
Enter negative values as negative numbers. b. Compute the residuals (to decimals). Enter negative
values as negative numbers.
c. Consider the following three scatter diagrams of the residuals
against the independent variable. Which of the following accurately
represents the data? 1.
2.
3.
Do
the assumptions about the error terms seem to be satisfied? d. Compute the standardized residuals. Enter negative values as
negative numbers.
e. Select a correct plot of the standardized residuals against . 1.
2.
3.
What
conclusions can you draw from this plot?
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Consider
the following data for two variables, x and y. Excel
File: data14-51.xlsx a. Consider the three scatter diagrams below.
Which
scatter diagram accurately represents the data? Does
the scatter diagram indicate any influential observations? b. Compute the standardized residuals for these data
(to decimals, if necessary). Enter negative values as negative
numbers.
Do
the data include any outliers? c. Compute the leverage values for these data (to decimals).
Enter negative values as negative numbers.
Does
there appear to be any influential observations in these data?
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Retail
chain Kroger has more than locations and is the largest
supermarket in the United States based on revenue. Kroger has invested
heavily in data, technology, and analytics. Feeding predictive models with
data from an infrared sensor system called QueVision to anticipate when
shoppers will reach the checkout counters, Kroger is able to alert workers to
open more checkout lines as needed. This has allowed Kroger to lower its
average checkout time from four minutes to less than seconds (Retail
Touchpoints). Consider
the data in the file Checkout. The file
contains observations. Each observation gives the arrival time
(measured in minutes before p.m.) and the shopping time (measured
in minutes).
a. Select the correct scatter diagram for arrival time as the independent
variable.
b. What does the scatter diagram developed in part (a) indicate about the
relationship between the two variables? There
appears to be a relationship
between the two variables. Does
there appear to be any outliers and/or influential observations? Observation appears
to be an observation with high leverage and may be very influential in terms
of fitting a linear model to the data. c. Using the entire data set, develop the estimated regression equation
that can be used to predict the shopping time given the arrival time
(to decimals). d. Use residual analysis to determine whether any outliers or influential
observations are present. Observation has
a standardized residual ,
indicating it is an outlier. e. After looking at the scatter diagram in part (a), suppose you were
able to visually identify what appears to be an influential observation. Drop
this observation from the data set and fit an estimated regression equation
to the remaining data (to decimals). Compare
the estimated slope for the new estimated regression equation to the
estimated slope obtained in part (c). Does this approach confirm the
conclusion you reached in part (d)? Explain. The
slope of the estimated regression equation is now as compared to a value of when this observation is included. Thus, we see that this
observation a
impact on the value of the slope of the fitted line and hence we that
it is an influential observation.
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The
Toyota Camry is one of the best-selling cars in North America. The cost of a
previously owned Camry depends upon many factors, including the model year, mileage,
and condition. To investigate the relationship between the car's mileage and
the sales price for a model year Camry, the following data show
the mileage and sale price for sales (PriceHub website).
Click on the datafile logo to reference the data.
If
your answer is zero, enter "". a. Select a scatter diagram with the car mileage on the horizontal axis
and the price on the vertical axis. 1. 2. 3. b. What does the scatter diagram developed in part (a) indicate about the
relationship between the two variables? c. Develop the estimated regression equation that could be used to
predict the price (s) (to decimals). d. Test for a significant relationship at the level of
significance (to decimals). -value . e. Did the estimated regression equation provide a good fit? f. Provide an interpretation for the slope of the estimated regression
equation (to decimals but dollar value to the nearest cent). Enter
negative values as negative numbers. The
slope of the estimated regression is . Therefore, every additional miles on the car's
odometr will result in a in
the predicted price. g. Suppose that you are considering purchasing a previously
owned Camry that has been driven miles. Using the
estimated regression equation developed in part (c), predict the price for
this car (round to nearest dollar). Is
this the price you would offer the seller?
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