Measurements

on young children in Mumbai, India, found this least-squares line for predicting height y from the arm span $\stackrel{⏜}{y}=6.4+0.93x$Measurements 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’t tell without seeing the data.

$\stackrel{⏜}{y}=6.4+0.93x$

Linear regression is commonly used for predictive analysis and modeling.

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,

$b=r\times \frac{s_y}{s_x}$

The correlation coefficient is, and the standard deviations of variables $X$ and $Y$ are $s_x$ and $s_y$ 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.