A researcher would like to predict GPA from a set of three predictor variables for a sample of 34 college students. Multiple linear regression analysis was utilized. Complete the following summary table
($\alpha$= .05) for the test of significance of the overall regression model:

Question

A researcher would like to predict GPA from a set of three predictor variables for a sample of 34 college students. Multiple linear regression analysis was utilized. Complete the following summary table 
($\alpha$= .05) for the test of significance of the overall regression model:

Quizplus · Accepted Answer

The Answer is There are three independent variables, so m = 3. There are 34 students, so n = 34.

df_reg= m = 3, df_res = n - m -1 = 34 - 3 - 1 = 30, df_total = n - 1 = 34 - 1 = 33.

SS_reg = MS_reg*df_reg = 6.5*3 = 19.5, SS_res = SS_total- SS_reg = 66 - 19.5 = 46.5.

MS_res = SS_res/df_res = 46.5/30 = 1.55

F = MS_reg/MS_re_s = 6.5/1.55 = 4.19; critical value = _.05F₃_,₃₀ = 2.92 < F, reject H₀.

There are three independent variables, so m = 3. There are 34 students, so n = 34. df<sub>reg</sub><sub> </sub>= m = 3, df<sub>res</sub> = n - m -1 = 34 - 3 - 1 = 30, df<sub>total</sub> = n - 1 = 34 - 1 = 33. SS<sub>reg</sub> = MS<sub>reg</sub>*df<sub>reg</sub> = 6.5*3 = 19.5, SS<sub>res</sub> = SS<sub>total</sub>- SS<sub>reg</sub> = 66 - 19.5 = 46.5. MS<sub>res</sub> = SS<sub>res</sub>/df<sub>res</sub> = 46.5/30 = 1.55 F = MS<sub>reg</sub>/MS<sub>re</sub><sub>s</sub> = 6.5/1.55 = 4.19; critical value = <sub>.05</sub>F<sub>3</sub><sub>,</sub><sub>3</sub><sub>0</sub> = 2.92 < F, reject H<sub>0</sub>.

A Researcher Would Like to Predict GPA from a Set α\alphaα

A Researcher Would Like to Predict GPA from a Set $\alpha$