You are reading a research article that summarizes the results of an experiment with 14 observations as:  β 0 = 4:1; β 1 = 2:5; σ= 0:5; r = 0:6: (a) Is there evidence that the independent and...

You are reading a research article that summarizes the results of an experiment with 14 observations as:  β₀
= 4:1; β₁
= 2:5; σ= 0:5; r = 0:6:

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

(b) What is the standard error of the estimate of the slope?

(c) Give a point estimate for a value of y if x = 3.

(d) Suppose the sample mean for the independent variable was x = 3. Give a 95% confidence interval for a new observation with this value of x.