A soda vendor at Louisiana State University football games observes that the warmer the temperature at game time the greater the number of sodas that are sold. Based on 32 home games covering five years, the vendor estimates the relationship between soda sales and temperature to be \(\hat{y}=-240+20 x\), where \(y=\) the number of sodas she sells and \(x=\) temperature in degrees Fahrenheit.

a. Interpret the estimated slope and intercept. Do the estimates make sense? Why or why not?

b. On a day when the temperature at game time is forecast to be \(80^{\circ} \mathrm{F}\), predict how many sodas the vendor will sell.

c. Below what temperature are the predicted sales zero?

d. Sketch a graph of the estimated regression line.