A research team collected data on n =452 participants in a longitudinal study. They observed that the average extent of rebellious symptoms observed at age 12 was 10.54, with an observed standard deviation of 3.42 (the divisor in the underlying variance calculation was n-1 ). They observed that the average measure of aggression at age 8 was 3.54, with an observed standard deviation of 0.64 (the divisor in the underlying variance calculation was n -1 ). The Pearson product moment correlation coefficient between the two variables was 0.32. The research team seeks to estimate the regression of extent of rebellious symptoms at age 12 on aggression at age 8.

a. Find the estimated regression equation of extent of rebellious symptoms on the aggression measure. Find the 95% confidence interval for the slope in this equation.

b. Complete the analysis of variance table for this regression

c. Use the least-squares prediction equation to predict the extent of rebellious symptoms at age 12 that will be shown by a participant who has a measure of aggression at age 8 to 5.0. Give a 95% prediction interval for the extent of rebellious symptoms at age 12 for this participant. (20 points)