Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_eur-inferential_statistics-104-en_eur-inferential_statistics-104-en
   name	eur-inferential_statistics-104-en
   section	Inferential Statistics/Regression/Equation, Inferential Statistics/Regression/Dummies
   type	string
   solution	""
   Type	Conceptual
   Program
   Language	English
   Level	Statistical Literacy

   Question

   A researcher investigates the criterion validity of a vocabulary test administered in grade 1 in order to predict reading comprehension in grade 4. From previous research she knows that there may be some test bias with respect to the native language of parents. Children whose parents are not Dutch native speakers are expected to show a different relationship between vocabulary and reading comprehension than children whose parents are native Dutch speaker. The results of the regression analyses (n=74, 12% non‐native parents) are given below. Note that the dummy variable “Native Dutch Parents” is 1 when the parents are Dutch native and 0 otherwise.

   

   Write down the regression equation for native Dutch parents and non‐native Dutch parents.

   
   

   Solution

   The general formulation of the regression line is: reading comprehension = $b_0 + b_1 ND parents + b_2 vocabulary + b_3 ND parents \times vocabulary$

   For Non‐native parents, the equation becomes: reading comprehension = $2 + 1.253 \times 0 + 0.614 \times vocabulary -0.23 \times 0 \times vocabulary$ reading comprehension = $2 + 0.614 vocabulary$

   For Native parents the equation becomes: reading comprehension = $2 + 1.253 \times 1 + 0.614 \times vocabulary -0.23 \times 1 \times vocabulary$ reading comprehension = $3.253 + 0.384 vocabulary$