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Chapter 14: Q.14.45 (page 570)

For two variables satisfying Assumptions 1-3 for regression inferences, the population regression equation is y=20-3.5x. For samples of size 10 and given values of the predictor variable, the distribution of slopes of all possible sample regression lines is a --------distribution with mean------- .

Short Answer

Expert verified

The distribution of slopes of all possible sample regression lines is a normal distribution with mean -3.5.

Step by step solution

01

Given Information

y=20-3.5x is the equation for population regression.

02

Explanation

A normal distribution with a mean of -3.5 exists for the slopes of all potential sample regression lines.

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Most popular questions from this chapter

In Exercises 14.48-14.57, we repeat the information from Exercises 14.12-14.21.

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

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

y=1.75+0.25x

Following are the data on the percentage of investments in energy securities and tax efficiency95%,伪=0.05 . find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the predictor variable.

Gas Guzzlers. The data from Exercise 14.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site. Specified value of the predictor variable: 3.0L.

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)-(f).

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%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 a 95%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).

Corvette Prices. Use the age and price data for Corvettes from Exercise 14.23.

a. compute the standard error of the estimate and interpret your answer

b. interpret your result from part (a) if the assumptions for regression inferences hold.

c. obtain a residual plot and a normal probability plot of the residuals.

d. decide whether you can reasonably consider Assumptions 1-3 for regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample sizes.)

14.75 High and Low Temperature. The data from Exercise 14.39for average high and low temperatures in January for a random sample of 50cities are on the WeissStats site.

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.
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