Homework 1

Due Thursday, 12 October, 1995

Meters johnson lewis 1 10 1.86 1.94 2 20 2.87 2.97 3 30 3.80 3.92 4 40 4.66 4.77 5 50 5.55 5.67 6 60 6.38 6.50 7 70 7.21 7.33 8 80 8.11 8.23 9 90 8.98 9.09 10 100 9.83 9.93

(a) For each runner, fit the elapsed time as a function of distance, using linear regression.

(b) Comment on the interpretation of the parameters in the model.

(c) For each runner, plot the residuals against the fitted values.

(d) Critically assess the usefulness of this model. What are its strengths? What are its weaknesses? Does the model raise any questions? How might the model be improved?

[Remark. These data were used on the 1992 PhD Preliminary Examination in Statistics. We shall be returning to these data from time to time during the course.]

2. ALR Exercise 1.5.

3. (a) ALR Exercise 1.2, parts 1.2.1-1.2.4.

(b) Which model (the linear model of 1.2.1 or the transformed model of 1.2.3) is better? How would you describe the relationship between pressure and temperature using your selected model? What do the coefficients mean?

(c) ALR Exercise 1.2, part 1.2.6.