(Please answer step-by-step. Typedwork preferable.)
1. The following matrix displaysthe bivariate correlations between family size (X), weekly grocerybill (Y), and income (Z) for a random sample of 50 families.
| X | Y | Z |
| X | 1.00 | 0.60 | 0.20 |
| Y | 0.60 | 1.00 | 0.30 |
| Z | 0.20 | 0.30 | 1.00 |
a. First, list the values of the 3 unique correlations,identifying the two variables in each correlation in some way.(rxy = ?; rxz = ? ryz = ?)
b. Which of the correlations is statistically significant at the.05 level? Be sure to record the information on which you basethese conclusions. (This implies you will need to perform ahypothesis test assessing whether each correlation is large enoughto suggest that a real association exists in the population fromwhich the sample was drawn.)
