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91Ó°ÊÓ

Smokers don’t live as long (on average) as nonsmokers, and heavy smokers don’t live as long as light smokers. You perform least-squares regression on the age at death of a group of male smokers y and the number of packs per day they smoked x. The slope of your regression line

(a) will be greater than 0

(b) will be less than 0

(c) will be equal to0

(d) You can’t perform regression on these data.

(e) You can’t tell without seeing the data.

Short Answer

Expert verified

The correct option is (b) will be less than0

Step by step solution

01

Given information

You run a least-squares regression on a group of male smokers' age at death yand the number of packs per day x

02

Concept

A regression line is a straight line that depicts the change in a response variable y when an explanatory variable x changes. By putting this x into the equation of the line, you may use a regression line to predict the value of y for any value of x

03

Explanation

Smokers (on average) have shorter lives than nonsmokers, and heavy smokers live shorter lives than light smokers. Assume you're conducting a least-square regression experiment on a sample of male smokers' death ages,Y, and the number of packs per day they smoked, XThe age number of survival days reduces as the number of packs smoked each day increases. In other words, as Xincreases, Ydecreases. To put it another way, Xand Yhave an antagonistic connection. We know that the sign of the slope and the sign of the correlation coefficient are the same. As a result, we can say that the slope of the regression line is negative. Hence, the slope of the regression line will be negative, which is less than 0

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