A research team sought to estimate the model E(Y)= B,+ B,x+ B,w. The variable Y is a measure of income of a participant observed at age 35; the variable x is a measure of the education expertise achieved by the participant at age 25; and the variable w is a measure of the healthiness of the participant's life style at age 30 (a larger number indicates a participant with a healthier life style). They observed values of y, x, and w on 900 participants. They found that the sample standard deviation of Y was 5.247 in units of $1000. The correlation between Y and w was 0.26; the correlation between Y and x was 0.58; and the correlation betweenx and w was 0.39. a) Compute the partial correlation coefficients ry and b) Compute the analysis of variance table for the multiple regression analysis of Y. Include the sum of squares due to the regression on w and the sum of squares due to the regression on x after including w. Test the null hypothesis that B = 0 at the 0.10, 0.05, and 0.01 levels of significance. c) Is a mediation model or an explanation model a better explanation of the observed results?