Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_vufgb-rsquared-010-en_vufgb-rsquared-010-en
   name	vufgb-rsquared-010-en
   section	Inferential Statistics/Regression/R squared, Inferential Statistics/Regression/Multiple linear regression, Inferential Statistics/Parametric Techniques/ANOVA, Inferential Statistics/Regression/Sum of squares
   type	schoice
   solution	FALSE, FALSE, FALSE, TRUE
   Type	Calculation, Interpreting output
   Program	SPSS
   Language	English
   Level	Statistical Thinking

   Question

   A multiple regression analysis is executed in SPSS.

   Underneath you will find the incomplete ANOVA table.

   Calculate the R-squared ($R^{2}$) of the model.

   

   
   
   1. FALSE: 0.33
   2. FALSE: 0.50
   3. FALSE: 0.60
   4. TRUE: 0.67
   
   

   Solution

   The formula for the $R^{2}$ is $\frac{(TSS-SSE)}{TSS}$. The $SSE = MSE \times df = 10 \times 20 = 200$.

   The corresponding $R^{2}$ is $\frac{(600-200)}{600} = \frac{400}{600} = 0.67$. Notice the 400 corresponds the the Regression Sum of Squares, which can also be determined by calculating $250 \times 1+150 \times 1$.

   
   
   1. Incorrect
   2. Incorrect
   3. Incorrect
   4. Correct