Question

1. A company that holds DVD distribution rights to movies previously released only in theaters wants to estimate the sales of DVDs based on box office success of a movie.  It will help this company to plan how many DVDs to produce and how to organize transportation.  A company collected records on recently released movies.  For each movie it recorded the box office gross (in $ millions), and number of DVDs sold (in thousands).
2. 1. Construct a model which allows predicting the number of DVDs sold (in thousands) based on box office gross (in $ millions).  Report your regression model below.
3. 2. Is this a valid model?  To receive credit, specify which hypotheses did you test, p-value, and your conclusion.
4. 3. Interpret the coefficients of the regression model.  Provide a clear, plain English interpretation.
5. 4. Characterize how good your model fits the data.  Explain the basis for your assessment.
6. 5.   For a movie with a box office gross of $55,000,000 ($55 Million), what are the projected DVDs sales?  Provide details of your computations.
7. 6. Copy-paste a residual plot, and report if residual plot indicates any problems with the regression model.  You need to address; normality of residuals, homoscedasticity/heteroscedasticity, and any patterns in the residual plot.

DVD Sales	Box Office
238.51	35
311.1	45.67
409.89	51.18
529.47	61.25
604.3	75.67
449.88	60.23
280.92	44.55
204.8	31.69
435.56	51.74
704.54	84.77
455.99	52.42
487.38	55.34
597.72	69.99
314.87	46.43
430.36	58.59
563.61	70.22
530.07	59.89
511.79	62.66
573.75	65.35
600.5	67.55
560.07	67.91
567.27	68.25
671.77	73.13
716.74	77.62
765.91	87.09
826.93	90.73
905.94	95.55
859.71	96.62
939.71	104.7
980.9	108.51

Answer 1

using minitab>stat>Regression

we have

Regression Analysis: DVD Sales versus Box Office

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 1192322 1192322 1102.58 0.00
Error 28 30279 1081
Total 29 1222601

Model Summary

S R-sq R-sq(adj) R-sq(pred)
32.8845 97.52% 97.43% 97.22%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -131.3 21.9 -6.00 0.000
Box Office 10.378 0.313 33.21 0.000 1.00

Regression Equation

DVD Sales = -131.3 + 10.378 Box Office

1. Regression Equation

   DVD Sales = -131.3 + 10.378 Box Office

2. we will use F test , F stat=1102.58   p-value = 0.000 since p value is less than 0.05 so the model is significant to use .
3. For every one million increase in box office , there is corresponding 10.38 thousand DVD sales increase
4. 97.43% variation in Dvd SAles can be explained by the BOx office
5. For a movie with a box office gross of $55,000,000 ($55 Million), the projected DVDs sales is  DVD Sales = -131.3 + 10.378*50 = 387.6
6. residual plot is

approximately all the residuals lies on the so we can say that the residuals follow normality