Chapter 14: Inferential Methods in Regression and Correlation

Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis $H_0:{\beta }_1=0$and the alternative hypothesis$H_{\mathrm{a}}:{\beta }_1\ne 0$. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?

Identify three statistics that can be used as a basis for testing the utility of a regression.

For a particular value of a predictor variable, is there a difference between the predicted value of the response variable and the point estimate for the conditional mean of the response variable? Explain your answer.

Generally speaking, what is the difference between a confidence interval and a prediction interval?

Fill in the blank: $\overline{x}$ is to$\mu$as$r$is to$\_\_\_\_$