A chemical reaction is run 12 times, and the temperature xi (in oC) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded:
Let β0 represent the hypothetical yield at a temperature of 0?C, and let β1 represent the increase in yield caused by an increase in temperature of 1oC. Assume that assumptions 1 through 4 on page 540 hold.
a. Compute the least-squares estimates and.
b. Compute the error variance estimate s2.
c. Find 95% confidence intervals for β0 and β1.
d. A chemical engineer claims that the yield increases by more than 0.5 for each 1oC increase in temperature. Do the data provide sufficient evidence for you to conclude that this claim is false?
e. Find a 95% confidence interval for the mean yield at a temperature of 40oC.
f. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40oC.