Examine the widths of the confidence intervals obtained in

Question

Learning the mechanics. A simple linear regression analysis for n = 20 data points produced the following results:

y^ = 2.1 + 3.4x

x‾ = 2.5

y‾ = 10.6

SS_xx = 4.77

SS_yy = 59.21

SS_xy = 16.22

(a) Find SSE and s².

(b) Find a 95% confidence interval for E(y) when x = 2.5. Interpret this interval.

(c) Find a 95% confidence interval for E(y) when x = 2.0. Interpret this interval.

(d) Find a 95% confidence interval for E(y) when x = 3.0. Interpret this interval.

(e) Examine the widths of the confidence intervals obtained in parts b, c, and d. What happens to the width of the confidence interval for E(y) as the value of x moves away from the value of x‾?

(f) Find a 95% prediction interval for a value of y to be observed in the future when x = 3.0. Interpret its value.