3 of 3 ID: MST.FET.R.MR.03.0020A [14 marks] A multiple regression model is to be constructed to predict the final exam score of a university student doing a particular course based upon their mid-term exam score, Final score Mid-term Score Hours studying Hours watching TV the average number of hours spent studying per week and the average number of hours spent watching television per week. per week per week 46 56 1 Data has been collected on 30 randomly selected individuals: show data 13 36 23 20 31 a) Find the multiple regression equation using all three explanatory variables. Assume that X, is mid-term score, X2 is hours studying per week and X is hours watching television per week. Give your answers to 3 decimal places. 55 37 18 26 mid-term score + hours studying + 98 92 19 hours watching television 24 62 63 3 22 b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis v rejected. 77 77 4 26 For parts c) and d), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables. 65 56 19 17 c) The explanatory variable that is most correlated with final score is: 36 28 10 26 73 77 11 22 O mid-term score O hours studying per week 60 50 19 26 O hours watching television per week 81 85 9 5 d) The explanatory variable that is least correlated with final score is: 31 23 15 11 O mid-term score 91 96 10 20 O hours studying per week 62 52 15 30 O hours watching television per week 66 53 13 13 e) The value of RZ for this model, to 2 decimal places, is equal to 52 38 5 32 f) The value of s. for this model, to 3 decimal places, is equal to 98 97 5 28 49 52 8 14 g) Construct a new multiple regression model by removing the variable average hours spent watching television per week. Give your answers to 3 decimal places. 56 34 20 6 The new regression model equation is: 45 28 17 10 y =+0 mid-term score +[ hours studying 54 53 10 21 h) In the new model compared to the previous one, the value of R2 (to 2 decimal places) is: 39 39 2 22 84 81 20 12 O increased O decreased 92 94 6 20 O unchanged 44 48 3 24 i) In the new model compared to the previous one, the value of s. (to 3 decimal places) is: 74 71 8 6 76 69 6 34 O increased O decreased 47 55 6 35 O unchanged 92 98 15 33 87 91 14 25