Question

the arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. an analysis was completed and the computer output is shown. using the computer output, what is the correlation? 0.630 0.649 0.794 0.806

Explanation:

Step1: Recall the relationship between correlation ($r$) and coefficient of determination ($r^{2}$)

The coefficient of determination is \(r^{2}\). If we assume the computer output gives \(r^{2}=0.630\), then \(r = \sqrt{r^{2}}\). But if we assume the computer output gives the slope - related formula. However, in regression, the formula for the slope \(b = r\frac{s_{y}}{s_{x}}\). But a more straightforward way: the value of the correlation coefficient \(r\) satisfies \(r^{2}\) (coefficient of determination). If we assume that the value among the options is calculated as follows.
We know that \(r^{2}\) (if we assume from regression output) and \(r\) has the same sign as the slope of the regression line. Since the slope of the regression line (from the scatter - plot trend, as arm span increases, foot length increases) is positive.
If we calculate \(r\) from the fact that in simple linear regression \(r^{2}\) is related to the proportion of variance explained. But another approach: the formula for the correlation coefficient \(r\) and the regression slope \(b\): \(b=r\frac{s_{y}}{s_{x}}\). But a more intuitive way (assuming standard output where \(r^{2}\) is not given directly but we use the property of \(r\)):
We know that \(r=\sqrt{r^{2}}\) (when slope is positive). If we assume that the value \(r = 0.794\) because if we consider the relationship between the variables in a positive - sloping regression (as in the scatter - plot) and typical values of \(r\) (where \(r^{2}=0.630\) would give \(r\approx0.794\) since \(0.794^{2}=0.630\))

Answer:

0.794