In a study of

the effect of temperature (x) on yield (y) of a chemical process, the following data were obtained:

x 25 26 27 28 29 30 31 32 33 34 35

y 11 15 14 17 20 18 19 23 24 23 28

(a) Plot the data and superimpose the linear regression of y on x fitted by least squares.

(b) Find the 95% condence intervals for $\displaystyle \beta$0 and $\displaystyle \beta$1.

(c) Predict the mean value of y at x = 30.5 and give an associated 95% confidence interval.

(d) Calculate a tolerance interval for y at x = 30.5 and give an associated 95% confidence interval.

(e) Why is the prediction interval smaller than the tolerance interval?

The problem im having with the above question is that iv never had to work out these things by hand before and show my working.... iv always been able to use R..... but now i want to understand the manual method :-)