1. As part of a drug stability monitoring exercise, measurements were made on the dissolution rate of the drug, per cent, at weekly intervals starting at time of manufacture (week 0 ) and continuing over a six month (25 week) period. The data were recorded as follows

1. A scatterplot of the data follows. Comment.
   
   The simple linear regression of Dissolution on Week was calculated, using Minitab. An excerpt from the Mintab output follows.
   
   The mean and standard deviation of the values 0 to 25 of Week were calculated as \(\bar{x}=12.5, s x=7.5\).
2. How do you interpret the value of the intercept coefficient?
3. Is the intercept significantly different from 100%? Explain.
4. How do you interpret the value of the slope coefficient?
5. Calculate a 95% confidence interval for the slope. How do you interpret the calculated interval?
6. Within what bounds would you expect the measured dissolution rate to be at 12 weeks? Use a \(95 \%\) prediction interval.
7. Routine monitoring of the dissolution rate of this drug involved making a measurement of the dissolution rate 3 months (12 weeks) after manufacture, using the regression results above as reference.

1. How would you react if the observed dissolution rate was $65 \%$ ? Explain.
2. How would you react if the observed dissolution rate was $55 \%$ ? Explain.

2. Data on the total annual compensation for the CEOs of 730 corporations for a recent year were recorded, along with the total annual sales of the same corporations. The graphs below shows a scatterplot of Compensation against Sales and a scatterplot of the logarithm (base 10) of Compensation against the logarithm (base 10) of Sales, along with Normal plots of Compensation, Sales, log of Compensation and \(\log\) of Sales.

1. Using a suitable diagram, explain why the logarithmic transformation might have been proposed for the two variables; refer to both scatterplots and Normal plots.
   (10 marks)
   The simple linear regression of \(\log\) (Comp) on log(Sales) was calculated, using Minitab. An excerpt from the Mintab output follows.
   
2. What hypothesis is tested by the t-ratio whose value is 15.18, corresponding to the coefficient of log(Sales)? Report on the statistical significance of the t-value and explain what it means in terms of the estimated value of the \(\log\) (Sales) coefficient.
   (5 marks)
3. What is measured by R-sq? Comment on the reported value of R-sq.
   (3 marks)
4. Comment on the apparently conflicting conclusions in the answers to parts
   (b) and (c).
   (5 marks)
5. Based on the calculated regression output provided, calculate a prediction interval for the logarithm of the total compensation of the CEO of a company with sales of \(\\) 500 \mathrm{~m}$.
6. How would you react if you learned that the CEO of a corporation with sales of \(\\) 500 \mathrm{~m}$ received total compensation of $8,000,000? Explain.

3. As part of a study of the relationship of the (second hand) Selling Value (IR£) of leased cars to Cost value (IR£), Age (days) and Mileage of the cars, a regression analysis of Selling Value on the other variables was conducted based on data from 41 Ford cars. Some details of the Selling Value case study are attached in Appendix 1. In the diagnostic plots, note that EStudRes stands for the deleted standardised residuals and that the highlighted case in all the diagnostics plots is Case 41.

1. Outline the four-step multiple linear regression model fitting and testing procedure.
   (10 marks)
2. Provide detailed illustrations of the application of each step of the procedure of part (a) using the information supplied in Appendix 1. Include explanations for the decisions to proceed with the second and third fits.
   (20 marks)
3. (i) Using the Second Fit regression, calculate the predicted selling value, with prediction interval, for a Ford car whose cost price, age and mileage were, respectively, £ 15,000, 1,000 days and 50,000 miles.

(ii) Using the Third (final) Fit regression, calculate the predicted selling value, with prediction interval, for a Ford car whose cost price, age and mileage were, respectively, £ 15,000, 1,000 days and 50,000 miles.

(iii) Comment on the comparison of the two predictions. Comment on the usefulness of either prediction interval.

(10 marks)

Price: $27.1

Solution: The downloadable solution consists of 13 pages, 1410 words and 13 charts.
Deliverable: Word Document