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Chapter 4: Q. 5 (page 192)

In Problems 3-5, answer true or false to each statement. Explain your answers.

If a line has a positive slope, y-values on the line decrease as thex-values decrease.

Short Answer

Expert verified

It is truethat if a line has a positive slope and its y-values drop as the x-values decrease.

Step by step solution

01

Concept Introduction

In a graph, if y-axis increases and x-axis decreases, then they are positively related, and if xdecreases, then ydeclines as well. The slope of a line graph on a left-to-right axis is positive as the line moves from left to right.

02

Explanation 

The formula for slope is,

m=change inychange inx=y2鈭�y1x2鈭�x1

The slope of the line segment between (2,5)and (0,1)is:

Calculation of the slope is as follows:

m=1-50-2=2

Whenever any point on the line increases by 1,yincreases by 2, and whenever any point on the line decreases by 1,ydecreases by 2.

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Most popular questions from this chapter

4.78 Gas Guzzlers. The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for 121vehicles. Those data are available on the Weiss Stats site.

a. Obtain a scatterplot for the data.

b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c) (f).

The data from Exercise 4.114for age and percentage of body fat for 18 randomly selected adults are on the Weiss Stats site.

a. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also parts (b)and (c)

b. Obtain the linear correlation coefficient.

c. Interpret the value of rin terms of the linear relationship between the two variables in question.

(a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables forx,y,e,e2,y^

(c) Determine which line fits the data points better according to the least-square criterion.

Shortleaf Pines. The data from Exercise 4.80for volume, in cubic feet, and diameter at breast height, in inches, for 70shortleaf pines are on the Weiss Stats site.

a) Decide whether finding a regression line for the data is reasonable. If so, then also do puts (b)-(d).

A Knight-Ridder News Service article in an issue of the Wichita Eagle discussed a study on the relationship between country music and suicide. The results of the study. coauthored by S. Stack and J. Gundlach, appeared as the paper "The Effect of Country Music on Suicide" (Social Forces, Vol. 71, Issue 1. Pp. 211-218). According to the article, " analysis of 49 metropolitan areas shows that the greater the airtime devoted to country music. the greater the white suicide rate," (Suicide rates in the black population were found to be uncorrelated with the amount of country music airtime.)

(a). Use the terminology introduced in this section to describe the statement quoted above.

(b). One of the conclusions stated in the journal article was that country music "nurtures a suicidal mood" by dwelling on marital status and alienation from work. Is this conclusion warranted solely on the basis of the positive correlation found between airtime devoted to country music and white suicide rate? Explain your answer.
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