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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

To find and interpret a confidence interval , at the specified confidence level 99%for the slope of the population regression line that relates the response variables to the predictor variable.


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.

Home Size and Value. The data from Exercise 14.38 for home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise 14.73 are on the WeissStats site.

Explain why the predictor variable is useless as a predictor of the response variable if the slope of the population regression line is 0.

1. Suppose that \(x\) and \(y\) are two variables of a population with \(x\) a predictor variable and \(y\) a response variable.

a. The distribution of all possible values of the response variable \(y\) corresponding to a particular value of the predictor variable \(x\) is called a distribution of the response variable.

b. State the four assumptions for regression inferences.
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