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Regression on R&D vs. Annual Profits

The data below record, for a sample of 10 firms, the number of staff employed in Research and Development (X), and annual profits in millions of pounds (Y).

X: [0,16,10,1,5,7,11,13,9,4]
Y: [12,60,30,11,15,18,32,45,25,14]

(a) Perform a linear regression of profits on R&D staff, and hence predict (giving confidence intervals) the profitability of a firm employing 20 R&D staff.

(b) It is now suggested that profitablity might be related more than linearly to the number of R&D staff. Regress profits on the square of R&D staff, and obtain an alternative prediction of the profitability of a firm employing 20 R&D staff.

(c) Compare the results of the two regressions. Which is to be preferred, and why? What should alert one to the weaknesses of the less preferred regression?

Solution Summary

Solution attaches a .doc file to show and explain these four questions on regression of a given table of data.

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