You are reading a research article that summarizes the results of an experiment with 15 observations as: β^ 0 = 2:8; β^ 1 = 20:6; σ^=1:2; r = 20:35: (a) Is there evidence that the independent and...

You are reading a research article that summarizes the results of an experiment with 15 observations as: β^₀
= 2:8; β^
₁
= 20:6; σ^=1:2; r = 20:35:

(a) Is there evidence that the independent and dependent variables are associated?

(b) Give a 90% confidence interval for the change in the expected value of y if x increases by 4 units.

(c) Give a point estimate for the value of y if x = 2.

(d) Suppose the sample mean for the independent variable was x = 0 and the sample standard deviation was s_x
= 3. Give a 95% confidence interval for a new observation with x = 2.