A small college selected 120 students at random from the new freshman class and measured their GPA at the end of their freshman year (Y), and their ACT score (X). The estimated regression line was:
Y = 2.114 +0.03883X
Where MSE=0.3883, and the values of s{Y} at corresponding X = 10,20,30 are 0.1965, 0.0829, 0.0882 respectively. Note: You may use R to find the values of the multiple for this problem. Data Source: "Applied Linear Statistical Models", Kutner, Nachtsheim, Neter, & Li.
(a) Calculate simultaneous/family-wise/overall 95% confidence intervals for the average value of Y at X = 10, and X = 30.