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Chapter 14: Q14.115 (page 585)

If p= 0, then the two variables under consideration are linearly __

Short Answer

Expert verified

p= 0 implies that the two variables are linearly uncorrelated.

Step by step solution

01

Basics

p(rho) is a statistical parameter for the entire population, determining whether the variables are linearly correlated or not.

Linear correlation means variables change at a constant rate, and their relationship is denoted by straight line curve.

02

Explanation

pindicates the magnitude of correlation in the variables' populations. It is between +1 and -1.

p =0 means that the variables are linearly uncorrelated.

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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 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 obtained in part (e).

14.103 High and Low Temperature. The data from Exercise $14.31$ for average high and low temperatures in January of a random sample, of $50$ cities are on the WeissStats site. Specified value of the predictor variable: $55 ° F$ .

In this Exercise 14.53, we repeat the information from Exercise 14.17.

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

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

role="math" localid="1652352243033" $\begin{array}{l} x & 2 & 2 & 3 & 4 & 4 \\ y & 3 & 4 & 0 & 2 & 1 \end{array}$ $\hat{y} = 5 - x$

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 $(b) - (f)$
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 inter. val that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.99 U.S. Presidents. The data from Exercise 14.35 for the ages at inauguration and of death of the presidents of the United States are on the WeissStats site. Specified value of the predictor variable: 53 years.

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

See all solutions

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