Find a 99 prediction interval for an observed value of y

Question

Consider the following summary statistics for data obtained in a simple linear regression analysis.

β^{^}₀ = 23.69

n = 7

MSE = 277.0

β^{^}₁ = 1.452

x‾ = 19.1

S_xx = 15.131

a. Find a 99% prediction interval for an observed value of Y when x = 19.25. Find the width of the resulting interval.

b. Find a 99% prediction interval for an observed value of Y when x = 18.10. Find the width of the resulting interval.

c. Explain why the width of the prediction interval in part (b) is greater than the width of the prediction interval in part (a).