In order to investigate the relationship between insurance companies’ annual cost-income ratios and the percentage of non-executive directors on the board, a sample of 12 medium sized insurance firms was taken and the following sums were calculated from the sample data:
∑x 5 440,
∑y 5 3.75,
∑xy 5 108.25:
where y represents the annual cost-income ratio and x represents the percentage of nonexecutive directors on the board.
(a) Taking the annual cost-income ratio (y) as the dependent variable and the percentage of non-executive directors on the board (x) as the independent variable, calculate the equation of the least-squares regression line.
(b) Using your estimated regression equation in part (a):
(i) Predict the annual cost-income ratio for a firm with a board consisting of ten directors, four of whom are non-executive directors.
(ii) Comment on the likely accuracy of your prediction in part (i).
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