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 number of active users Facebook has: Adjusted R Std. Error of Model R R Square Square the Estimate .8229 .659 8.45078 a. Predictors: (Constant), SandP500 .675 Standardized Coefficients Beta Unstandardized Coefficients Model B Std. Error 1 (Constant) - 76.447 17.371 SandP500 .011 a. Dependent Variable: Facebook -4,401 6.452 Sig. .000 .000 .071 .822 Adjusted R Std. Error of Model R R Square Square the Estimate .822 .676 .642 8.66745 a. Predictors: (Constant), Monthly Active Users (millions), SandP500 1 Standardized Coefficients Beta 1 -1.028 Unstandardized Coefficients B Std. Error -69.175 67.301 .065 055 .003 .023 Sig. 317 .250 Model (Constant) SandP500 Monthly Active Users (millions) a Dependent Variable: Facebook .752 1.186 .112 .071 .912 Based on the results of these regressions: The addition of the number of active users variable greatly improves the fit of the model and the variable is clearly related to the dependent variable. The addition of the number of active users variable does not much improve the fit of the model, but the variable is clearly closely related to the dependent variable. The addition of the number of active users variable does not much improve the fit of the model, and the variable is not clearly related to the dependent variable. The addition of the number of active users variable greatly improves the fit of the model, but the variable is clearly not related to the dependent variable.

Answer 1

As we can see from the first table where we have only one variable SandP500, the p-value for the t test of significance of coefficient is 0 which is very low and therefore suggest that the variable is significant when it is the only variable in regression.

Now when we add another variable, we can see from the second table of coefficient analysis for the two independent variables, the p-values are 0.25 and 0.912 which are both high and so the variables when both added are not significant individually. Therefore the addition of number of monthly active users variable does not much improve the fit of the model and the variable is not clearly related to the dependent variable here. (as the individual test statistic result has p-value very high )