Suppose we want to use Twitter activity to predict box officereceipts on the opening weekend for movies. Assuming a linearrelationship, the Excel output for this regression model is givenbelow.
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Excel output:
SUMMARY OUTPUT | | | | | | | |
| | | | | | | | |
Regression Statistics | | | | | | | |
Multiple R | 0.9879 | | | | | | | |
R Square | 0.9760 | | | | | | | |
Adjusted R Square | 0.9712 | | | | | | | |
Standard Error | 1830.236 | | | | | | | |
Observations | 7 | | | | | | | |
| | | | | | | | |
ANOVA | | | | | | | | |
| df | SS | MS | F | Significance F | | | |
Regression | 1 | 6.81E+08 | 6.81E+08 | 203.153 | 3.06E-05 | | | |
Residual | 5 | 16748821 | 3349764 | | | | | |
Total | 6 | 6.97E+08 | | | | | | |
| | | | | | | | |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% |
Intercept | 6808.105 | 854.968 | 7.962991 | 0.000504 | 4610.339 | 9005.87 | 4610.339 | 9005.87 |
Twitter Activity | 0.0503 | 0.00353 | 14.25318 | 3.06E-05 | 0.041205 | 0.059338 | 0.041205 | 0.059338 |
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(a) State the regression equation for thisproblem.
(b) Interpret the meaning of b0 andb1 in this problem.
(c) Predict the box office receipts on theopening weekend for a movie that has a Twitter activity of110,000.
(d) At the 0.05 level of significance, is thereevidence of a linear relationship between the Twitter activity andthe box office receipts on the opening weekend for a movie?
(e) Construct a 95% confidence intervalestimate of the population slope β1. Interpret theconfidence interval estimate.
(f) How useful do you think this regressionmodel is for predicting the box office receipts on the openingweekend for a movie?
