Question

A colleague of yours is completing a final report on the causes of the frequency of cyberbullying. In this report, she is asked to identify the causes that most strongly impacted the frequency of cyberbullying. She conducts an OLS regression. What statistic do you advise her to use in her discussion? Why?

* Please show work *

Answer 1

We use t and F statistic to conduct the significance of OLS regression model.

The t statistic is computed by dividing the estimated value of the parameter by its standard error.  This statistic is a measure of the likelihood that the actual value of the of the coefficient of OLS regression model is not zero. The larger the absolute value of t, the less likely that the actual value of the coefficient could be zero and the associated variable would be a significant variable in estimating the frequency of cyberbullying.

The F statistic test the overall significance of the OLS regression model.  Specifically, they test the null hypothesis that all of the regression coefficients are equal to zero.  This tests the full model against a model with no variables and with the estimate of the dependent variable being the mean of the values of the dependent variable.  The F value is the ratio of the mean regression sum of squares divided by the mean error sum of squares.  Its value will range from zero to an arbitrarily large number. A large value of F (based on degree of freedom) would imply that at least some of the regression parameters are nonzero and that the regression equation does have some validity in fitting the data to estimate the frequency of cyberbullying.