QUESTION
i. Use MS Excel Data Analysis ToolPak to perform a multiple regression analysis using Quality as the response variable and Helpfulness and Clarity as the explanatory variables. Write down the corresponding coefficient estimates and provide the regression output.
j. Perform an F-test for the overall usefulness of the model in part i) using a 5% significance level. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.
k. Test manually if the Clarity variable is significant in the model in part i). Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.
l. Using the adjusted R2 criterion, does including Clarity as an additional predictor variable improve the model in part i)? Explain why it is better to use the adjusted R2 over the R2 to determine if the addition of this new variable improves the model.
Regression Statistics | ANOVA | |||||||
Multiple R | 0.998544859 | df | SS | MS | F | Significance F | ||
R Square | 0.997091836 | Regression | 2 | 255.2639136 | 127.6319568 | 62229.00058 | 0 | |
Adjusted R Square | 0.997075813 | Residual | 363 | 0.744514614 | 0.002051004 | |||
Standard Error | 0.045288017 | Total | 365 | 256.0084282 | ||||
Observations | 366 | |||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -0.020353502 | 0.010520921 | -1.934574223 | 0.0538193 | -0.04104311 | 0.000336106 | -0.04104311 | 0.000336106 |
helpfulness | 0.538358378 | 0.007216008 | 74.60611907 | 2.8925E-222 | 0.524167949 | 0.552548808 | 0.524167949 | 0.552548808 |
clarity | 0.465505241 | 0.00707634 | 65.78333849 | 8.6445E-204 | 0.451589474 | 0.479421009 | 0.451589474 | 0.479421009 |