A chemical engineer studied the effect of the amount of surfactant and time on

clathrate formation. Clathrates are used as cool storage media. The dataset is

Clathrate.txt. Here are the variables:

y: Clathrate formation (mass %)

x1: Amount of surfactant (mass %)

x2: Time (minutes)

0 10 7.5 0 50 15 0 85 22 0 110 28.6 0 140 31.6 0 170 34 0 200 35 0 230 35.5 0 260 36.5 0 290 38.5 0 10 12.3 0 30 18 0 62 20.8 0 90 25.7 0 150 32.5 0 210 34 0 270 35 0.02 10 14.4 0.02 30 19 0.02 60 26.4 0.02 90 28.5 0.02 120 29 0.02 210 35 0.02 30 15.1 0.02 60 26.4 0.02 120 27 0.02 150 29 0.05 20 21 0.05 40 27.3 0.05 130 48.5 0.05 190 50.4 0.05 250 52.5 0.05 60 34.4 0.05 90 46.5 0.05 120 50 0.05 150 51.9 

(a) Fit a multiple linear regression model relating clathrate formation to these

regressors.

(b) Test if the model you t in part (a) is significant. What conclusions can you

draw?

(c) Use t tests to assess the contribution of each regressor to the model. Discuss

your findings.

(d) What is the R2 for model? Compare it to the R2 for the simple linear regression

model relating clathrate formation to time. Discuss your results.

(e) Find a 95% confidence interval for the regression coefficient for time for both

models in part (d). Discuss any differences.

(f) Construct a normality plot of the residuals from the full model. Does there

seem to be any problem with the normality assumption?

(g) Construct and interpret a plot of the residuals versus the predicted response.

(h) Find the values of the Cook's distance and construct the Cook's Distance plot.