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Chapter 14: Q 5 (page 588)

Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0:β1=0and the alternative hypothesisHa:β1≠0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?

Short Answer

Expert verified

Useful for making predictions.

Step by step solution

01

Step 1:Given information

A hypothesis test for the slope of the population regression line with the null hypothesis and the alternative hypothesis

02

Step 2:Explaination

We can say that the regression equation is useful for making predictions.

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Most popular questions from this chapter


Find a95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

a. Obtain a point estimate for the mean tax efficiency of all mutual fund portfolios with6%of their investments in energy securities.

b. Determine a95%confidence interval for the mean tax efficiency of all mutual fund portfolios with6%of their investments in energy securities.

c. Find the predicted tax efficiency of a mutual fund portfolio with 6%of its investments in energy securities.

d. Determine a 95%prediction interval for the tax efficiency of a mutual fund portfolio with 6%of its investments in energy securities.

we repeat the data and provide the sample regression creations

a. Determine the standard error of the estimate

b. Construct of residual plot.

c. Construct a nommal probability plot of the residuals.

x243
y357

y^=2+x

Gas Guzzelrs. Use the data on the WeissStats site for gas mileage and engine displacement for 121vehicles referred to in Exercise 14.41

a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).

b. Decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

In this Exercise 14.52, we repeat the information from Exercise 14.16.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

x1344y13-135 y^=14-3x

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(h).
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95% Te confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).
14.100 Movie Grosses. The data from Exercise 14.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Specified value of the predictor variable: S 100 million.
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