A chemical reaction is run 12 times, and the temperature xi (in —¦C) 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 1—¦C. Assume that assumptions 1 through 4 on page 540 hold.
a. Compute the least-squares estimates β0 and β1.
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 1—¦C 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 40—¦C.
f. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40—¦C.

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12 Σ(xi-M2 = 6032.0 65.0 y=29.05 12 12