4. Run a multiple regression where the dependent variable is ratings and the ind

Question

4. Run a multiple regression where the dependent variable is ratings and the independent variables are star and fact. Use data from CBC only. CBC Management has several questions: a. Which has more impact on a movie’s rating: Being fact-based or having one star? How much does each of these factors change the ratings? b. How well does this regression analysis explain the ratings? Justify your answers referring to the relevant figures. c. Are either, both, or neither of the independent variables significantly related to the ratings at 95% confidence? Justify your answers referring to the relevant figures.

Observation Network Month Day Rating Fact Stars 1 BBS 1 1 15.6 0 1 2 BBS 1 7 10.8 1 0 3 BBS 1 7 14.1 0 1 4 BBS 1 1 16.8 1 1 5 BBS 2 1 14.3 1 1 6 BBS 2 1 17.1 1 1 7 BBS 3 1 15.8 0 0 8 BBS 3 7 16.2 1 0 9 BBS 4 7 12.6 0 1 10 BBS 5 1 13.5 0 1 11 BBS 5 7 15.6 0 0 12 BBS 5 1 12.1 0 1 13 BBS 5 1 15.8 1 0 14 BBS 9 7 15 1 0 15 BBS 9 7 16.3 0 0 16 BBS 9 7 13.3 0 1 17 BBS 10 7 10.8 0 1 18 BBS 10 7 14.4 1 0 19 BBS 11 7 14.4 1 1 20 BBS 11 7 13.6 1 0 21 ABN 1 7 14.6 0 0 22 ABN 1 2 10.8 0 1 23 ABN 1 7 16.2 0 0 24 ABN 1 2 12.8 0 0 25 ABN 1 7 16 0 1 26 ABN 2 7 18.9 0 1 27 ABN 2 2 17.6 1 1 28 ABN 3 7 19.5 1 1 29 ABN 3 2 16.9 1 0 30 ABN 3 7 16.3 0 1 31 ABN 3 7 15.8 1 0 32 ABN 3 7 17.1 0 1 33 ABN 3 2 15.8 0 0 34 ABN 3 7 16 1 0 35 ABN 3 2 11.7 0 1 36 ABN 4 2 14.2 0 0 37 ABN 4 7 18.1 0 0 38 ABN 4 2 15.2 0 0 39 ABN 4 7 13.3 0 1 40 ABN 4 7 15.5 1 0 41 ABN 4 2 16.6 1 0 42 ABN 5 7 16.3 1 0 43 ABN 5 7 16.5 0 1 44 ABN 5 2 16.8 1 0 45 ABN 9 7 15.4 0 1 46 ABN 9 2 14.7 0 0 47 ABN 9 7 15.5 0 0 48 ABN 9 2 14.7 1 0 49 ABN 10 7 15.9 1 0 50 ABN 10 7 13.8 1 0 51 ABN 10 2 14.9 0 1 52 ABN 11 7 12.9 0 1 53 ABN 11 2 15.4 1 0 54 ABN 11 7 14.5 0 2 55 ABN 12 7 12.6 0 2 56 ABN 12 2 11.8 0 0 57 ABN 12 2 12.8 0 0 58 ABN 12 7 16.8 0 1 59 CBC 1 7 14 0 1 60 CBC 1 1 11.3 1 0 61 CBC 2 1 12.4 0 1 62 CBC 2 7 12.9 1 0 63 CBC 3 1 13.2 1 0 64 CBC 3 7 12.8 1 0 65 CBC 4 1 12.4 1 1 66 CBC 4 7 13.2 0 1 67 CBC 5 1 17.5 1 0 68 CBC 5 7 11.6 0 0 69 CBC 5 7 12.1 0 0 70 CBC 6 1 15.6 0 0 71 CBC 6 7 12.1 0 1 72 CBC 6 1 11.8 0 0 73 CBC 7 7 12.3 0 0 74 CBC 7 1 14.2 1 1 75 CBC 8 7 11.6 0 0 76 CBC 8 1 13.3 1 0 77 CBC 8 1 13.6 1 0 78 CBC 9 1 12.4 0 1 79 CBC 9 1 13.8 1 0 80 CBC 9 7 11.9 1 0 81 CBC 10 1 14.6 0 0 82 CBC 10 1 15.8 1 1 83 CBC 10 1 15.4 0 1 84 CBC 11 1 12.8 0 1 85 CBC 11 7 12.8 0 0 86 CBC 12 1 15.1 0 0 87 CBC 12 1 11.4 0 1 88 CBC 12 1 19.1 1 0

Explanation / Answer

Here we wnat to run the multiple regression where the dependent variable is ratings and the independent variables are star and fact.

using minitab

Step 1) first enter the given data in minitab columns

step 2) Click on Stat>>>Regression >>>General Regression...

Response: Rating ( because here rating is our dependent variable)

Model: Select Facts and then select Stars

then click on OK so we get the following output

General Regression Analysis: Rating versus Fact, Stars

Regression Equation

Rating = 13.9935 + 1.01298 Fact + 0.0850413 Stars

Coefficients

Term Coef SE Coef T P
Constant 13.9935 0.371775 37.6398 0.000
Fact 1.0130 0.457093 2.2161 0.029
Stars 0.0850 0.414909 0.2050 0.838

Summary of Model

S = 2.00145 R-Sq = 5.74% R-Sq(adj) = 3.53%
PRESS = 364.370 R-Sq(pred) = -0.87%

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P
Regression 2 20.747 20.747 10.3734 2.58960 0.080963
Fact 1 20.578 19.674 19.6737 4.91130 0.029353
Stars 1 0.168 0.168 0.1683 0.04201 0.838091
Error 85 340.492 340.492 4.0058
Lack-of-Fit 2 8.237 8.237 4.1187 1.02889 0.361917
Pure Error 83 332.255 332.255 4.0031
Total 87 361.239

From the above output the multiple regression model is

Rating = 13.9935 + 1.01298 Fact + 0.0850413 Stars

Since the coefficient of Facts (1.01298) is greater than the coefficient of Stars(0.0850413 ) so that Facts are more important than Stars

The change of Facts and Stars are same as there coefficients.

b) R-square = 5.74% so just 5.74% of the variation in Rating is explain by the independent variables(Facts and Stars)

c).since p-value of Stars is  0.838 is very large from 0.05 so we can say that Stars is not significance variable at 95% confidence.

but p-value of Facts is 0.029 < 0.05 so we can say that at 95% confidence facts is significantly related with Rating.

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