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Measurements

on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span y=6.4+0.93xMeasurements are in centimeters (cm).

By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is

(a) greater than zero.

(b) less than zero.

(c) 0.93

(d) 6.4

(e) Can鈥檛 tell without seeing the data.

Short Answer

Expert verified

The correct option is (a) greater than zero.

Step by step solution

01

Given information

y=6.4+0.93x

02

Concept

Linear regression is commonly used for predictive analysis and modeling.

03

Calculation

A least-squares line for predicting height Y from arm span X was discovered using measurements on young children in Mumbai, India. The units of measurement are centimeters (cm). We can see that the slope of the regression line is 0.93, which is positive, from the presented regression line.

We know that,

b=rsysx

The correlation coefficient is, and the standard deviations of variables X and Y are sx and sy Because standard deviations are always positive, the slope's sign is the same as the correlation coefficient's sign. Because the slope of the given regression line is positive, we may assume that the sign of the correlation coefficient is similarly positive.

Therefore, option (a) is the correct one.

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