Question

the scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. an analysis was completed and the computer output is shown. using the computer output, what is the equation of the least-squares regression line?

○ (hat{y}=4.317 + 0.310x)
○ (hat{y}=0.310 + 4.317x)
○ (hat{y}=-14.71 + 1.585x)
○ (hat{y}=1.585 - 14.71x)

Explanation:

Step1: Recall the form of the least - squares regression line

The equation of the least - squares regression line is \(\hat{y}=a + bx\), where \(a\) is the y - intercept and \(b\) is the slope.

Step2: Analyze the options

We know that the y - intercept \(a\) is the value of \(\hat{y}\) when \(x = 0\). Looking at the scatter - plot, when \(x\) (handspan) is around \(17\), \(\hat{y}\) (number of pretzels) is around \(12\).
For the equation \(\hat{y}=-14.71 + 1.585x\), when \(x = 17\), \(\hat{y}=-14.71+1.585\times17=-14.71 + 26.945 = 12.235\) which is close to the value on the scatter - plot.
For \(\hat{y}=4.317 + 0.310x\), when \(x = 17\), \(\hat{y}=4.317+0.310\times17=4.317 + 5.27=9.587\) (too low).
For \(\hat{y}=0.310 + 4.317x\), when \(x = 17\), \(\hat{y}=0.310+4.317\times17=0.310 + 73.389 = 73.699\) (way too high).
For \(\hat{y}=1.585-14.71x\), when \(x = 17\), \(\hat{y}=1.585-14.71\times17=1.585 - 250.07=-248.485\) (negative and wrong).

Answer:

\(\hat{y}=-14.71 + 1.585x\)