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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^=β0+β1x.

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 β0and β1such that the conditional mean of the response variables is β0+β1xfor 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^=β0+β1x.

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Most popular questions from this chapter

we repeat the data and provide the sample regression equations for Exercises a.Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

In this Exercise 14.49, we repeat the information from Exercises 14.13.

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.

x312y-40-5 y^=1-2x

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

In Exexcises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your 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% 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 obfained in part (e).
14.102 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 14.101 are on the WeissStats site. Specified value of the predictor variable: 3000 sq. ft.

Crown-Rump Length. In the article "The Human Vomeronasal Organ. Part II: Prenatal Development" (Joumal of Anatomy, Vol. 197, Issue 3, pp. 421-436), T. Smith and K. Bhatnagar examined the controversial issue of the human vomeronasal organ, regarding its structure, function, and identity. The following table shows the age of fetuses (x), in weeks, and length of crown-rump (y), in millimeters.
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