Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_vufgb-rsquared-020-en_vufgb-rsquared-020-en
   name	vufgb-rsquared-020-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 performed in SPSS. Below is 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 $TSS = 600$. The $SSE = MSE ˜times df = 10 ˜times 20 = 200$.

   The $R^{2}$ is then $\frac{(600-200)}{600} = \frac{400}{600} = 0.67$. Note that the 400 in the numerator corresponds to the Regression Sum of Squares, which can also be captioned by $250 \times 1+150 \times 1$ calculate.

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