2. We have data on a number of movies that includes the USGxoss (in S), the Budg
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2. We have data on a number of movies that includes the USGxoss (in S), the Budget (S), the Run Time (minutes), and the average number of Stars awarded by reviewers. We want a regression model to predict USGross (i.e., how much money the movie makes). Parts of the regression output computed in Excel look like this Source Regression Residual Sum of Squares df Mean Square F-Ratio 224995 249799 74998.4 34.8 116 2153.44 Dependent variable is USGross(S) R-squared=47.4% R-squared (adjusted) 46.0% s-46.41 with 120 -4-116 degrees of freedom ariale Coefficient SE(Coeff) t-Ratio P-Value Intercept -22.9898 25.70 Budget() 1.13442 0.1297 Stars 0.895 0.3729 0.0001 4.24 s0.0001 24.9724 Run Time-0.403296 0.2513 1.60 0.1113 a) Write the multiple regression equation. b) What is the interpretation of the coefficient of Budget in this regression model? c) What is the null hypothesis tested for the coefficient of Stars in this table? What is the t statistic corresponding to this test? What is the P-value corresponding to this t-statistic? Complete the hypothesis test using both approaches we've talked about in class - confidence interval and actual t-statistic. Do you reject the null hypothesis (explain in one sentence)? d) What is the null hypothesis tested for the coefficient of Run Time? Why is this t-statistic negative? Complete the hypothesis test using both approaches we've talked about in class - confidence interval and actual t-statistic. Do you reject the null hypothesis (explain in one sentence)1 e) What is the R-squared for this regression? What does it mean? f) Why is the "Adjusted R-Squared" in the table different from the "R-Squared"? g) What is the F-statistic value for this regression? What null hypothesis can you test with it?Explanation / Answer
a. USGross =-22.9899+1.13442*Budget+24.9724*Stars-0.403296*Run Time
b. With the increase in one unit of Budget it would increase USGross by 1.13442 keeping all others being unchanged
c. The null hypothesis being tested for coefficient of star is that the value 24.9724 is different from zero or it is being a chance factor which is determined by the p-value. A low p-value (< 0.05) indicates that we can reject the null hypothesis which means a predictor that has a low p-value is likely to be a meaningful addition to model because changes in the predictor's value are related to changes in the response variable. The p-value is <0.0001, so we can reject null hypothesis and confirm stars is significant with USgross.
d. The null hypothesis being tested for coefficient of Run time is -0.403296. Since Run time is having negative relation with USgross, the t value = coefficient/SE= -0.403296/0.2513=-1.60. The null hypothesis is that the coefficient -0.403296 is equal to zero. Here we can accept the null hypothesis as the p-value is greater than 0.05 which means the value of the coefficient is by chance factor and dropping the variable would not impact much on USGross.
e. R-square is 47.4% which means the regression model is able to capture 47.4% of the variation and rest 52.6% being leftover.
f. R-square value increase with the inclusion of new independent variables but adjusted R-squared provides an adjustment to the R-squared statistic such that an independent variable that has a correlation to Y increases adjusted R-squared and any variable without a strong correlation will make adjusted R-squared decrease which is why it is different
g. The F-statistic is 34.8. The value of Prob(F) is used to test the null hypothesis and if Prob(F) value is less than 0.01 then there is 1 chance in 100 that all of the regression parameters are zero.
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