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In the simple linear regression model, the ____________ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.
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What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?
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________________ is used to test the hypothesis that the values of the regression parameters B0, B1, B2, ... Bq are all zero.
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Suppose that the sales manager of a large automotive parts distributor wants to estimate as early as April the total annual sales of a region. On the basis of regional sales, the total sales for the company can also be estimated. If, based on past experience, it is found that the April estimates of annual sales are reasonably accurate, then in future years the April forecast could be used to revise production schedules and maintain the correct inventory at the retail outlets.

Several factors appear to be related to sales, including the number of retail outlets in the region stocking the company's parts, the number of automobiles in the region registered as of April 1, and the total personal income for the first quarter of the year. Five independent variables were finally selected as being the most important (according to the sales manager). Then the data were gathered for a recent year. The total annual sales for that year for each region were also recorded. Note in the following table that for region 1 there were 1,739 retail outlets stocking the company's automotive parts, there were 9,270,000 registered automobiles in the region as of April 1, and so on. The sales for that year were $37,702,000. Data file is given at Data_automobile.xlsx.

Use the .05 significance level. What percent of the variation is explained by the regression equation?

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See Q4.

Expected regression equation is

Sales = -19.671511 -0.000628611*Outlets + 1.7399011* Cars + 0.409935351*Income+ 2.035712563*Ages-0.034446171*Bosses

Can you conclude at least one of the coefficients in the above equation is not zero?

Conduct a global test of hypothesis and use critical value approach at the .05 significance level, where

H0: beta1=beta2=beta3=beta4=beta5=0

H1: Not all the beta_i are 0.

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See Q5

Which coefficients of regression equations are zeros? Conduct individual hypothesis tests at the .05 significance level.

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Q7-Q10 use Excel spreadsheet: Data_hw_Oscar.xlsx.

Given b0 = -0.4054 and b1=0.0836 in the logistic regression, what is logit of movie "Places in the Heart"?

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See Q7. Given b0 = -0.4054 and b1=0.0836 in the logistic regression, what is predicted probability of winner for movie "Places in the Heart"?

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See Q7. Given b0 = -0.4054 and b1=0.0836 in the logistic regression, what is log likelihood for movie "Places in the Heart"?
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See Q7. are b0 = -0.4054 and b1=0.0836 optimal values to maximize the total likelihood? If not, what should be b0 and b1?

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