a. Construct a regression equation in which total U.S. box office grosses are pr

Question

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

Explanation / Answer

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.

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