A brewer is interested in the amount spent by alcohol consumers per week (y) on alcohol and the factors which influence

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A Brewer Is Interested In The Amount Spent By Alcohol Consumers Per Week Y On Alcohol And The Factors Which Influence 1 (124.69 KiB) Viewed 20 times

A brewer is interested in the amount spent by alcohol consumers per week (y) on alcohol and the factors which influence this. Data has been collected on the amount spent (in thousands of rands), the income of the head of the household (x1) (in hundreds of thousands of rands per year) and the household size (x2) for ten families and the results are presented in Table 1. Table 1 Income of head of Household Amount spent per week household size 20 6 1 17 5 2 5 10 1 0 14 4 3 25 2 8 10 5 14 21 1 19 17 1 32 29 2 17 14 3 Σ y = 135 Σx =151 Σx, = 22 The linear model y=B₁ + B₁x₁ + ₂x₂ + & where & is the error term was proposed. 151 22 10 X'X= 151 2849 320; (X'X)¹ = -0.029664024 -0.145562562 0.001236846 0.868164399 -0.029664024 -0.145562562 0.001236846 0.05767675541 0.001784302 and 22 320 66 Y'Y=2657 a) Using the usual notation used in your module, calculate X'Y. (3) b) Find estimates of B, B₁ and ₂ of the regression coefficients of the proposed model and interpret them. (8) c) Construct the ANOVA table and test the hypothesis regarding the overall regression model at the 5 percent level. (10) d) Regardless of the findings from c), determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the regression model that should be used in this problem. (12) (4) e) Find the variance inflation factor (VIF) and interpret the value.