Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_vufsw-r_squared_change-1028-en_vufsw-r_squared_change-1028-en
   name	vufsw-r squared change-1028-en
   section	inferential statistics/regression/multiple linear regression/r squared change
   type	schoice
   solution	TRUE, FALSE, FALSE, FALSE
   Type	interpreting output
   Program	NA
   Language	english
   Level	statistical literacy

   Question

   We are researching the effect of hours of training and attitude on the performance of a specific skill (e.g. the number of goals scored). For this purpose, we run 2 regressions with performance as the dependent variable.

   In the first regression, hours of training and attitude are included as independent variables, while in the second regression, we also add the interaction between hours of training and attitude as an independent variable.

   We perform the F-test for the R² change to decide whether to choose the second regression instead of the first one.

   The following regression equation refers to the second regression. Which of the following statements on the R² change and the F-test of the R² change is plausible?

   performance = 1.23^* + 0.112 × attitude + 0.531^* × hours + 0.167^* × attitude × hours

   * indicates a statistically significant effect

   
   
   1. TRUE: R² change = 0.051, F(1,537)=4.2537, P-value=0.0396
   2. FALSE: R² change = 0.051, F(1,537)=4.2537, P-value=0.396
   3. FALSE: R² change = -0.001, F(1,537)=4.2537, P-value=0.0396
   4. FALSE: R² change = -0.001, F(1,537)=4.2537, P-value=0.396
   
   

   Solution

   These numbers indicate an increase in the R² due to the inclusion of the interaction in the regression and a statistically significant F-test for the R² change. The interaction effect between attitude and hours is statistically significant (see the * that is placed next to it in the regression equation). In the case of a single interaction, the F-test of the R² change always agrees with the t-test of the interaction. When a variable is included in the regression the R² always increases, at least by a tiny bit. In no whatsoever case can the R² decrease due to the inclusion of a variable in the regression. Moreover, the interaction effect between attitude and hours is statistically significant (see the * that is placed next to it in the regression equation). In the case of a single interaction, the F-test of the R² change always agrees with the t-test of the interaction.

   Language
   English

   M&T Dimitris Pavlopoulos
   Default value

   M&T Moderation
   Default value

   
   
   1. True
   2. False
   3. False
   4. False