Data on the relationship between the lifetime milk yield of dairy cows and the age at which the cows first calved are given in the table below. Age ( months) 22 28 32 34 24 36 27 33 26 Lifetime milk yield (Liters) 18747 17995 17842 17358 18673 17650 18730 17991 18056 a. Find the least squares regression line for the data. That is, calculate the slope, b and the intercept a, of the regression of lifetime milk yield (Liters) on age at first calving (months), and give the linear regression equation as 'Y = a + bX'. (4 marks) b. Give a brief interpretation of all the components (b, X and Y) of the regression equation, within the context of this study. (4 marks) c.. Predict the lifetime milk yield (Liters) for a cow which first calved at 30 months of age. (1 mark) d. Calculate the analysis of variance for the dependent variable to test the significance of the overall relationship. In your answer, clearly state the null hypothesis and give a conclusion. (8 marks) e. Can you conclude that the regression coefficient, b, you calculated above, is significantly different from zero at a = 0.05? (3 marks) f. Calculate the coefficient of correlation, r, and test whether it is significantly different from zero. (3 marks) 9. Calculate the coefficient of determination, R and provide its interpretation within the context of this study? (2 marks)