Homework Soursea Construct a regression equation in which total US box offi
a. Construct a regression equation in which total U.S. box office grosses are predicted using the other variables
b. Determine if the overall model is significant using an alpha level of .05
c. Determine the range of plausible values for the change in box office grosses if the average ticket price were to be increased by $1. Use a confidence level of 95%.
d. Calculate the variance inflation factor for each of the independent variables. Indicate if multicollinearity exists between any two independent variables.
e. Produce the regression equation suggested by your answer to part d.
Data:
| Year | Grosses | Admissions | AvePrices | Screens |
| 2005 | 8.99 | 1.40 | 6.41 | 37092 |
| 2004 | 9.5 | 1.53 | 6.21 | 36012 |
| 2003 | 9.49 | 1.57 | 6.03 | 35361 |
| 2002 | 9.52 | 1.63 | 5.8 | 35170 |
| 2001 | 8.41 | 1.49 | 5.65 | 34490 |
| 2000 | 7.67 | 1.42 | 5.39 | 35567 |
| 1999 | 7.45 | 1.47 | 5.06 | 36448 |
| 1998 | 6.95 | 1.46 | 4.69 | 33418 |
| 1997 | 6.37 | 1.39 | 4.59 | 31050 |
| 1996 | 5.91 | 1.34 | 4.42 | 28905 |
| 1995 | 5.49 | 1.26 | 4.35 | 26995 |
| 1994 | 5.4 | 1.29 | 4.08 | 25830 |
| 1993 | 5.15 | 1.24 | 4.14 | 24789 |
| 1992 | 4.87 | 1.17 | 4.15 | 24344 |
| 1991 | 4.8 | 1.14 | 4.21 | 23740 |
| 1990 | 5.02 | 1.19 | 4.22 | 22904 |
| 1989 | 5.03 | 1.26 | 3.99 | 21907 |
| 1988 | 4.46 | 1.08 | 4.11 | 21632 |
| 1987 | 4.25 | 1.09 | 3.91 | 20595 |
Solution
Here dependent variable Y is grosses
and the independent variables are ,
X1 : Admissions
X2 : AvePrices
X3 : Screens
All this we can done using MINITAB.
Steps : STAT --> Regression --> Regression --> Response Y --> predictor X1,X2 and X3 --> Options : variance inflation factors and PRESS ans predicted R-square --> Results second option --> Storage first three options --> ok
Construct a regression equation in which total U.S. box office grosses are predicted using the other variables
The regression equation is
Y = - 6.90 + 5.36 X1 + 1.51 X2 - 0.000033 X3
Determine if the overall model is significant using an alpha level of .05
Predictor Coef SE Coef T P VIF
Constant -6.9047 0.1862 -37.09 0.000
X1 5.3614 0.2628 20.40 0.000 6.2
X2 1.51172 0.04687 32.25 0.000 5.1
X3 -0.00003336 0.00000924 -3.61 0.003 10.0
S = 0.0738531 R-Sq = 99.9% R-Sq(adj) = 99.8%
PRESS = 0.150085 R-Sq(pred) = 99.76%
Analysis of Variance
Source DF SS MS F P
Regression 3 62.761 20.920 3835.58 0.000
Residual Error 15 0.082 0.005
Total 18 62.843
Here the P-value for all the three factors is less than 0.05 so we reject H0 at 5% level of significance.
Conclude that the overall model is significant at 5% level of significance.
A 99.8% R-sqadj indicates that when ever we observe a variation in the value of y, 99.8% of it is due to the model (or due to change in x1,x2 and x3) and only .2% is due error or some unexplained factor. That is this data fits well to the linear model.
For ANOVA we test the hypothesis that
H0 : beta = 0 Vs H1 : beta 0
In fact F is nothing but T-square.
A low p-value suggest that beta plays a significant role in the model, this is just reassurance of the t-test.
