Regression Analysis
Question 1
Estimate the model SalesTrop = β0 + β 1×PriceTrop + β 2×PriceMM + β 3×PriceDom + β 4×Feature + β 5×Display +
Qn1.1 The following are the regression analysis tables.
| Regression Statistics | |
| Multiple R | 0.818424409 |
| R Square | 0.669818514 |
| Adjusted R Square | 0.654810265 |
| Standard Error | 11811.44376 |
| Observations | 116 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 5 | 31131717954 | 6.23E+09 | 44.63002 | 5.99E-25 |
| Residual | 110 | 15346122395 | 1.4E+08 | ||
| Total | 115 | 46477840349 |
| Coefficients | Standard Error | t Stat | P-value | |
| Intercept | 54434.01686 | 10151.90119 | 5.361953 | 4.59E-07 |
| PriceTrop | -21274.83138 | 2606.694783 | -8.16161 | 5.97E-13 |
| PriceMM | 8796.880907 | 2830.093242 | 3.108336 | 0.002395 |
| PriceDom | 898.2071683 | 3047.525898 | 0.294733 | 0.768753 |
| Feature | 938.3844498 | 2644.852137 | 0.354797 | 0.723421 |
| Display | 19576.16684 | 3195.870786 | 6.125456 | 1.43E-08 |
Qn1.2
The R-squared value of the regression is 0.669818514 implying that about 67 percent of the variation in the SalesTrop variable can be explained by the explanatory variables.
Qn1.3
The p-values of PriceDom and Feature coefficients are 0.768753 and 0.723421 respectively. Basing on the p-values, the two coefficients are statistically insignificant since the p-values are less than the significance level of 0.05.
Qn1.4
The coefficient of PriceTop is -21274.83138, while its p-value is 5.97E-13. The coefficient is statistically significant since it has a small p-value. The Negative sign on the coefficient implies that it has a negative effect on the dependent variable (William& Delvin, 1988). An increase in in PriceTop reduces the SalesTrop by that value.
Question 2
Estimating the model log(SalesTrop) = β0 + β 1×log(PriceTrop) + β 2×log(PriceMM) + β 3×Display + ε
The following are the regression analysis tables
| Regression Statistics | |
| Multiple R | 0.890644868 |
| R Square | 0.793248282 |
| Adjusted R Square | 0.787710289 |
| Standard Error | 0.150713754 |
| Observations | 116 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 3 | 9.760764 | 3.253588 | 143.2375 | 3.51E-38 |
| Residual | 112 | 2.544039 | 0.022715 | ||
| Total | 115 | 12.3048 |
| Coefficients | Standard Error | t Stat | P-value | |
| Intercept | 5.059883418 | 0.097157 | 52.07969 | 2.46E-80 |
| log(PriceTop) | -2.6047888 | 0.171565 | -15.1825 | 5.96E-29 |
| log(PriceMM) | 0.559682055 | 0.177894 | 3.146146 | 0.002119 |
| Display | 0.277055241 | 0.040366 | 6.863575 | 3.92E-10 |
Qn2.2
The value of the coefficient of log(PriceTop) is -2.6047888. The value is negative and therefore implies that an increase in the scores of the variable reduces the value of log(SalesTrop) by the coefficient value. The logarithm function transforms data on the variable in a bid to view the data in a different perspective. Similarly, the transformation returns a normal-like data if then original dataset was skewed (Chao-Ying, 2002).
Qn2.3
The value of the coefficient of log(PriceMM) is 0.559682055. The value is positive, meaning that an increase in the values of the log(PriceMM) increases the value of the dependent variable.
Qn2.4
The value of the coefficient of Display is 0.277055241. The coefficient has a p-value less than the significance level of 0.05, implying that it is statistically significant. Similarly, the coefficient is positive meaning that an increase in the Display values increases the log(SalesTrop).
Works Cited
Chao-Ying Joanne Peng, Kuk Lida Lee & Gary M. Ingersoll. An Introduction to Logistic Regression Analysis and Reporting, The Journal of Educational Research, 96:1, 3-14, (2002) DOI: 10.1080/00220670209598786
Douglas Curran-Everett. Explorations in statistics: the log transformation, Advances in Physiology Education, 10.1152/advan.00018.2018, 42, 2, (343-347), (2018).
William S. Cleveland & Susan J. Devlin. Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting, Journal of the American Statistical Association, 83:403, 596-610, (1988) DOI: 10.1080/01621459.1988.10478639