For the correlation matrix in Problem 31 in Chapter 10, find the proportion of variance in the weekly grocery bill (Y) determined by family size (X) alone, by income (Z) alone, and by family size and income together.

Data From Problem 31 Chapter 10

The following is a correlation matrix among family size (X), weekly grocery bill (Y), and income (Z) for a random sample of 50 families.

a. Which of the correlations are significant at the .05 level?
b. Calculate the partial correlation between family size and grocery bill, holding income constant, and then determine if this partial correlation is significant.
Discuss the difference between the simple correlation r_XY and the partial correlation r_XY.Z.

Transcribed Image Text:

X Y Z X 1.00 .60 .20 Y .60 1.00 .30 Z .20 .30 1.00