Answer Happy

6. (a) A random sample of 6 houses is drawn. The area of the house (1, in mº) and electricity consumption (y, in $100) are recorded below: I, (in mº) 120 100 140 110 120 90 y, in $100) 7 8 139 105 i. Calculate the rank correlation coefficient, 's, for the data. [3 marks) ii. Find the least squares regression line for predicting electricity consumption. [4 marks] (b) The admission office of a university would like to develop a regression model of student's first year GPA (y) on four admission test scores denoted by 11, 12, 13 and x4, respectively. Twenty-five first year students are selected at random and a multiple regression equation is fitted with the following results: ANOVA Table Source df MS F Regression 5.6722 b d f Residual a Total 7.6453 24 SS с 11 X2 Coefficients Standard Error Intercept -0.760594 0.641177 0.001976 0.013542 0.021241 0.009344 Is 0.017504 0.008856 14 0.017965 0.008972 i. Find the fitted multiple regression line from the above results. [1 mark) ii. Calculate the missing values a tof in the ANOVA table. [3 marks) iii. Calculate the adjusted coefficient of determination. [2 marks] iv. Test the overall significance of the regression model at the 5% level of sig- nificance. [3 marks) v. The regression line will be further revised so as to exclude those independent variables which are not significant. Determine those independent variables, if there any, to be excluded at the 5% level of significance. (4 marks)