Question

Below are the results of two regressions. The first is to predict the stock price of Facebook based on the level of the S&P 500 index. The second is to predict the stock price of Facebook based on the level of the S&P 500 index and the return on the S&P 500 index: Adjusted R Std. Error of Model R R Square Square the Estimate .8222 .659 8.45078 a. Predictors: (Constant), SandP500 .675 Standardized Coefficients Beta sig Unstandardized Coefficients Model B Std. Error (Constant) -76.447 17.371 SandP500 .071 .011 a. Dependent Variable: Facebook 1 -4.401 6.452 .000 .000 .822 1 Adjusted R Std. Error of Model R R Square Square the Estimate .8499 .721 .690 8.22410 a. Predictors: (Constant), SandP500_Return, SandP500 Standardized Unstandardized Coefficients Coefficients Model Std. Error Beta (Constant) -88.221 18.180 SandP500 .078 .011 .851 SandP500_Return -16.089 74.242 -027 a. Dependent Variable: Facebook Based on these results, the addition of the S&P 500 Return variable: B Sig. .000 1 -4.853 6.818 .000 - 217 .831 CU Produced a regression that is impossible to compare to the original regression (which included only the variable for the level of the S&P 500). Produced a regression that is clearly worse than the original regression (which included only the variable for the level of the S&P 500). O Produced a regression that is clearly better than the original regression (which included only the variable for the level of the S&P 500). Produced a regression that is better in some ways and worse in some ways than the original regression (which included only the variable for the level of the S&P 500). a

Answer 1

From the first table of significance, we see that the p-value for the SandP500 is 0 which means that individually the independent variable SandP500 is significance.

Now from the second table, we see that as we add SandP500_Return to the model, the p-value for that variable for the t test is given to be 0.831, therefore individually its clear that the dependent variable is not dependent on the independent variable but if we see the adjusted R² here we can see that there is clearly an increase in the value, and therefore this a better regression on an overall level. Therefore D is the correct answer here - in some ways it has improved in other it has made it worse.