1. Given a regression equation = 2.35 + 6.82x, with n=18 and a correlation coefficient, r = 0.42, conduct a hypothesis test to determine if the regression relationship between x and y is statistically significant at the 5% level of significance. What conclusion can be drawn from the hypothesis test? [10]

2. A business analyst believes that capital utilisation (as measured by inventory turnover) has a direct effect on a company's earnings yield. To examine this belief, the analyst randomly surveyed nineJSE-listed companies and recorded their inventory turnover and their earning yield.

Inventory turnover	3	5	4	7	6	4	8	6	5
Earnings yield	10	12	8	13	15	10	16	13	10

a) Graphically display the relationship between inventory turnover and earnings yield for the sample of ninecompanies. What relationship can be observed? [2] b) Calculate a linear regression equation to express the relationship between the inventory turnover and earnings yields of companies. [4] c) Construct the correlation coefficient between inventory turnover and earnings yield. Does this value support the business analyst's view? Comment. [1] d) Find the coefficient of determination between earnings yield and inventory turnover.[1]

e) Test the significance of the correlation coefficient between inventory turnover and earnings yield. Conduct a hypothesis test at the 5% level of significance. What conclusion can be drawn? [5] f) What earnings yield can a company expect to achieve if they have an inventory turnover of six next year?