91Ó°ÊÓ

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span x $\stackrel{Áåœ}{y}=6.4+0.93x$Measurements are in centimeters (cm).

In addition to the regression line, the report on the

Mumbai measurements says that $r^2=0.95.$This suggests that

(a) although arm span and height are correlated, arm span does not predict height very accurately.

(b) height increases by $0.95=0.97cm$ for each additional centimeter of arm span.

(c) $95\%$ of the relationship between height and arm span is accounted for by the regression line.

(d) $95\%$ of the variation in height is accounted for by the regression line.

(e) $95\%$ of the height measurements are accounted for by the regression line.

Step by step solution

01

Given information

$$\begin{gathered} \stackrel{Áåœ}{y}=6.4+0.93x \\ {r}^2=0.95 \end{gathered}$$

02

Concept

Linear regression is commonly used for predictive analysis and modeling.

03

Explanation

A least-squares line for predicting height $Y$from arm span $X$was discovered using measurements on young children in Mumbai, India. $\stackrel{Áåœ}{y}=6.4+0.93x$Measurements are in centimeters (cm).

The coefficient of determination $r$ is the percentage of variation in $Y$values that can be explained by Yon $X\text{'}s$least-squares regression line.

The least-squares regression of height on arm span accounts for $95$percent of the variation in height in this case, with $r^2=95$Therefore, option (a) is the correct.

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