A fire department official thinks that the number of fires raises as the temperature decreases, since more fires are lit to stay warm. The following statistics are collected:
Temperature: 40° 35° 30° 25° 20° 15° 10° 5°
Number of Fires: 28 32 35 39 51 55 56 66
Employ simple regression to predict the number of fires from the temperature.
(a) Is there sufficient evidence to support official's claim (namely, that the regression slope is negative)? Report your hypotheses, test statistic, P-value, and conclusion.
b) Determine a 99% confidence interval for the average number of fires when the temperature is 18°.