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Chapter 12: Q.1.2 (page 777)

Give the equation of the least-squares regression line. Define any variables you use.

Short Answer

Expert verified

The equation of the least-squares regression line is y^=-1.19311+0.0287280x.

Step by step solution

01

Given Information

02

Explanation

In the question that variable xbe the number of the years since 1700and the variable y be the U.S. population in the years 1790to 1880. Thus, the general equation will be as:

y^=a+bx

And the slope and the constant of the regression line is give in the previous question as:

a=-1.19311

b=0.0287280

Thus, the regression line is as:

y^=a+bx

⇒y^=-1.19311+0.0287280x

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Most popular questions from this chapter

Which of the following would provide evidence that a power law model of the form y=axbwhere b≠0andb≠1, describes the relationship between a response variable yand an explanatory variable x.

(a) A scatterplot of yversus xlooks approximately linear.

(b) A scatterplot of ln yversus xlooks approximately linear.

(c) A scatterplot of yversus ln xlooks approximately linear.

(d) A scatterplot of ln yversus ln xlooks approximately linear.

(e) None of these.

In Chapter 3, we examined data on the body weights and backpack weights of a group of eight randomly selected ninth-grade students at the Webb Schools. Some Minitab output from least-squares regression analysis for these data is shown.

2. With such a small sample size, it is difficult to check several of the conditions for regression inference. Assume that the conditions are met. Construct and interpret a 95%confidence interval for the slope of the population regression line.

About 1100high school teachers attended a weeklong summer institute for teaching AP classes. After hearing about the survey in Exercise 50, the teachers in the AP Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted for a sample size of 100teachers. One of the questions on the survey was Do you have any tattoos on your body?

One of the first decisions the class had to make was what kind of sampling method to use.

(a) They knew that a simple random sample was the “preferred” method. With teachers in 40different sessions, the class decided not to use an SRS. Give at least two reasons why you think they made this decision.

(b) The AP Statistics class believed that there might be systematic differences in the proportions of teachers who had tattoos based on the subject areas that they taught. What sampling method would you recommend to account for this possibility? Explain a statistical advantage of this method over an SRS.

Which of the following statements about the t distribution with degrees of freedom df is (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom.

III. As df increases, the t distribution approaches the standard Normal distribution.

(a) I only (c) III only (e) I, II, and III

(b) II only (d) I and II

Inference about the slope βof a least-squares regression line is based on which of the following distributions?

(a) The t distribution with n-1degrees of freedom

(b) The standard Normal distribution

(c) The chi-square distribution with n-1degrees of freedom

(d) The t distribution with n-2degrees of freedom

(e) The Normal distribution with mean μand standard deviationσ

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