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Chapter 14: Q. 14.5 (page 560)

Based on a sample of data points, what is the best estimate of the population regression line?

Short Answer

Expert verified

The best estimate of the population regression line is written as,y^=尾0+尾1x.

Step by step solution

01

Given information

The best estimate of the population regression line.

02

Explanation

The variables under investigation meet the regression inference assumptions.

Line of population regression: There are constants 尾0and 尾1such that the conditional mean of the response variables is 尾0+尾1xfor each value of xfor the predictor variable.

The sample regression line is the best estimate of the population regression line and is written as,

y^=尾0+尾1x.

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Most popular questions from this chapter

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.

What statistic is used to estimate

a. The y-intercept of the population regression line?

b. The slope of the population regression line?

c. The common conditional standard deviation, 蟽, of the response variable?

To find and interpret a confidence interval, at the specified confidence level 90%for the slope of the population regression line that relates the response variables to the predictor variable.

In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

y=14-3x

Identify two graphs used in a residual analysis to check the Assumptions 1-3 for regression inferences, and explain the reasoning behind their use:
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