Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_eur-inferential_statistics-113-en_eur-inferential_statistics-113-en
   name	eur-inferential_statistics-113-en
   section	Inferential Statistics/Parametric Techniques/Correlations/Pearson
   type	schoice
   solution	FALSE, TRUE, FALSE, FALSE
   Type	Conceptual
   Program
   Language	English
   Level	Statistical Literacy

   Question

   We predict Y from X1 using linear regression analysis. The Pearson correlation between X1 and Y is r = 0.40 and $s_Y^2$ = 100. When we add a second variable, X2, to the regression model we get $R^2$ = 0.25. How much additional variance is explained by the addition of X2 compared to the regression model with only X1?

   
   
   1. FALSE: 0.15 or 15%
   2. TRUE: 0.09 or 9%
   3. FALSE: 0.40 or 40%
   4. FALSE: 0.25 or 25%
   
   
   1. This answer is incorrect
   2. This is the correct answer! The explained variance in Y based on X1 alone equals $0.40^2$ = 0.16 or 16%. When X2 is added to the model, the total proportion of variance explained equals 0.25 of 25%; the increase is 0.25 - 0.16 = 0.09 or 9%.
   3. This answer is incorrect
   4. This answer is incorrect