6. (a) A random sample of 6 houses is drawn. The area of the house (x, in mº) and electricity consumption (y, in $100) a

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6 A A Random Sample Of 6 Houses Is Drawn The Area Of The House X In Mo And Electricity Consumption Y In 100 A 1 (52.51 KiB) Viewed 21 times

6. (a) A random sample of 6 houses is drawn. The area of the house (x, in mº) and electricity consumption (y, in $100) are recorded below: , (in m2) 120 100 140 110 120 90 y, (in $100)7 8 139 105 i. Calculate the rank correlation coefficient, T., 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 24, respectively. Twenty-five first year students are selected at random and a multiple regression equation is fitted with the following results: ANOVA Table Source SS df MS F Regression 5.6722 b d f Residual Total a с e 7.6453 24 13 Coefficients Standard Error Intercept -0.760594 0.641177 0.001976 0.013542 0.021241 0.009344 0.017504 0.008856 0.017965 0.008972 i. Find the fitted multiple regression line from the above results. [1 mark] ii. Calculate the missing values a to fin 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