"A. The QuestionThe Movie Receipts shows the data on the amount of money a movie makes at theaters in the first yearafter the movie is released to the public. The independent variables are; the total production cost, totalpromotion cost and the total book sales. The dependent variable is the first year box office receipts.These are the office receiptsTotalTotal Promotion First year boxproduction Cost Total Book office receiptscost ($million) ($million) Sales ($ million) ($ million)8.5 5.1 4.7 85.112.9 5.8 8.8 106.35.2 2.1 15.1 50.210.7 8.4 12.2 130.63.1 2.9 10.6 54.83.5 1.2 3.5 30.39.2 3.7 9.7 79.49.0 7.6 5.9 91.015.1 7.7 20.8 135.410.2 4.5 7.9 89.3This report will conduct a multiple regression using the three variables; the total productioncost, total promotion cost and the total book sales to determine the first year box officereceipts, to determine how important each variable to thefirst year box office receipts.B. Regression results1. Using all three explanatory variables:x : Total production cost1 x : Total Promotion Cost2 x : Total Book Sales3 y: the dependent variable, First year box office receiptsRegression results from Excel's Data Analysis – Regression function using 99% confidence(significance level ? = 0.01):SUMMARY OUTPUTRegression StatisticsMultiple R 0.983254R Square 0.966789Adjusted RSquare 0.950183Standard Error 7.541009Observations 10ANOVA df SS MS F Significance FRegression 3 9932.463 3310.821 58.22062 7.91266E-05Residual 6 341.2009 56.86681Total 9 10273.66 StandardCoefficients Error t Stat P-valueIntercept 7.676029 6.760228 1.135469 0.299491Total production cost($million) 3.661604 1.117751 3.275866 0.01691Total Promotion Cost($million) 7.621051 1.657317 4.598426 0.003698Total Book Sales ($ million) 0.828468 0.539359 1.536023 0.17544a. Adjusted R Square 0.950183.This shows a very good fit for the data, which isextremely high.b. Based on the regression coefficients, the estimated regression equation isˆ y ? 7.6760 ? 3.6616x ? 7.6211x ? 0.8285x1 2 3 c. Significance of the regression:The "F Statistic" at 58.22062is much larger than the-5 "Significance F" statistic 0.00006 or 7.91266×10 . This means we can reject the nullhypothesis H : ß = ß = ß = 0 and conclude that at least one of the regression0 1 2 3 coefficients is not equal to zero.Significance of the coefficients:For each coefficient ß, H : ß = 0, H : ß ? 00 i a i This will use a p-valuetest:rejection criterion:Reject H if p =a, that is if p = 0.010 intercept: p-value = 0.299491> 0.01we accept H : ß = 00 0 coefficient of x :p-value = 0.01691> 0.01we accept H : ß = 01 0 1 coefficient of x :p-value = 0.003698< 0.01we rejectH : ß = 02 0 2 coefficient of x :p-value = 0.17544< 0.01 we acceptH : ß = 03 0 3 Therefore, we can drop intercept and total book sales from the regression since its coefficient isnot significantly different from zero and seems to have no significant effect on the first year boxoffice receipts.Although the total promotion cost is not significantly different from zero, its p-value is not muchgreater than the significance level 0.01. Accordingly, we will keep the total promotion cost inthis second iteration of the regression using only x and x as explanatory variables and see1 2 whether it should be discarded.2. Using two explanatory variables:x : Total production cost1 x : Total Promotion Cost2 y: the dependent variable, First year box office receiptsRegression results from Excel's Data Analysis – Regression function using 99% confidence(significance level ? = 0.01):SUMMARY OUTPUTRegression StatisticsMultiple R 0.976591R Square 0.953729Adjusted R Square 0.940509 Standard Error 8.240757Observations 10ANOVA Significancedf SS MS F FRegression 2 9798.294 4899.147 72.14167 2.13E-05Residual 7 475.3706 67.91008Total 9 10273.66StandardCoefficients Error t Stat P-valueIntercept 11.84821 6.764977 1.751405 0.12334Total production cost($million) 4.228244 1.153028 3.667077 0.007995Total Promotion Cost($million) 7.43611 1.806318 4.116722 0.004478a. Adjusted R Square 0.976591. This shows a very good fit for the data, which is extremelyhigh.b. Based on the regression coefficients, the estimated regression equation isy ˆ ? 11.8482 ? 4.2282x ? 7.4361x1 2 c. Significance of the regression:The "F Statistic" at 72.14167is much larger than the-5 "Significance F" statistic 0.00002 or 2.13×10 . This means we can reject the nullhypothesis H : ß = ß = ß = 0 and conclude that at least one of the regression0 1 2 3 coefficients is not equal to zero.Significance of the coefficients:For each coefficient ß, H : ß = 0, H : ß ? 00 i a i This will use a p-valuetest:rejection criterion:Reject H if p =a, that is if p = 0.010 intercept: p-value = 0.1233> 0.01we accept H : ß = 00 0 coefficient of x :p-value = 0.007995< 0.01we reject H : ß = 01 0 1 coefficient of x :p-value = 0.004478< 0.01 we reject H : ß = 02 0 2 Consequently, we can conclude that total production cost and total production cost areimportant determinants of first year box office receiptsand the regression equation calculated isa useful predictor for it.But in this iteration of the regression the intercept is rejected as it isnot significantly different from zero.The regression equation for these data isˆ y ? 4.2282x ? 7.4361x1 2 C. ResidualsTo examine whether the assumptions of the regression model hold, we can see the regressionresiduals for this final version of the regression to see whether they satisfy the criteria thatresiduals should have a mean of 0 and a constant variance or standard deviation. This is the table of predicted values of y (first year box office receipts), the residuals, and thestandardized residuals of the regression: "