Question

Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (°F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Y^ = −114.05+2.17X. On one of the observed days, the temperature was 82 °F and 66 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Y^, when the temperature is 82 °F. Enter your answer as a whole number, rounding if necessary. Y^ = 34 ice bags Using the predicted value you just found, compute the residual at this temperature. residual =

Answer 1

Our model is

$\hat{y} = 2.17 x + -114.05$

When x=82 degrees F,

$\hat{y} = 2.17 (82) + -114.05 = 63.89$

We round up to

Answer: 64 bags

Not sure why it says y^=34 in the question; I'm ignoring that.

The residual is the difference between the actual y and the predicted y,

$e = y - \hat{y} = 66 - 64 = 2$

Answer: 2