III. Mathematical Modeling
RD Model
Having completed the regression analysis for TID, we turned to the task of developing a formula for RD by using the same techniques. The predictor variables used were PREL, AREL, and RD1 (brand loyalty). From these variables, we used a multiple regression analysis and derived the following table and formula:
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Regression Statistics |
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Multiple
R |
0.978525574 |
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R Square |
0.957512299 |
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Adjusted
R Square |
0.956783938 |
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Standard
Error |
0.056004573 |
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Observations |
179 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
3 |
12.36989885 |
4.123299616 |
1314.612994 |
9.7505E-120 |
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Residual |
175 |
0.548889625 |
0.003136512 |
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Total |
178 |
12.91878847 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
16.12999601 |
0.444521299 |
36.28621627 |
2.37432E-83 |
15.25268317 |
17.00730884 |
15.25268317 |
17.00730884 |
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Prel |
-16.44445198 |
0.444138495 |
-37.02550482 |
1.0431E-84 |
-17.32100931 |
-15.56789465 |
-17.32100931 |
-15.56789465 |
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Arel |
0.779630225 |
0.02694443 |
28.93474561 |
1.33291E-68 |
0.726452359 |
0.832808091 |
0.726452359 |
0.832808091 |
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RD1 |
0.533422048 |
0.016432467 |
32.46147126 |
5.6314E-76 |
0.500990725 |
0.565853371 |
0.500990725 |
0.565853371 |
RD =
-16.44*PREL + .7796*AREL + .5334RD1 + 16.13
We performed all of our standard sanity checks, which yielded microscopic P-values, and a R-square value of .96 indicating a near perfect formula. With TID and RD mathematically defined, we were now able to complete our model for firm demand.