A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm) , and the foot length, in cm , for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
The figure presents a scatterplot in a coordinate plane. The horizontal axis is labeled Foot Length, in centimeters, and the numbers 18 through 34, in increments of 2, are indicated. The vertical axis is labeled Height, in centimeters, and the numbers 150 through 190, in increments of 10, are indicated. There are 65 data points in the scatterplot, and a trend line is given as follows. Note that all values are approximate. The data points begin in the lower left part of the plane at the point with coordinates 19 comma 160. The data points trend upward and to the right and end with the coordinates 33 comma 190. The least-squares regression line begins at the point 18 comma 153, and slants upward and to the right at a constant rate to end at the point 35 comma 197.
Term Coef (SE) Coef T -Value P -Value
Constant 105.08 6.00 17.51 0.000
Foot length 2.599 0.238 10.92 0.000
S=5.90181 R–sq=65.42%
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .
(b) The standard deviation of the residuals is s=5.9 . Interpret the value in context.
Unit 2 Progress Check: FRQ
Aubree Flores