Business Statistics and Quantitative Analysis Project, homework help

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ECON7300: Statistical Project Assignment, Semester 2, 2016 Instructions for Dataset 1: Simple Regression Analysis (30 marks) Paul is a student currently enrolled in Economics. He decided to try to improve his results. He needed to know the secret of success for university students. After many hours of discussing with more successful students, he postulated a theory: the longer one studied, the better one’s grade. To test the theory, he took a random sample of 96 students in an economics subject and asked each student to report the average amount of time he/she studied economics and the final mark received. The variables in the dataset are:  Study time (X, in hours)  Final mark (Y, out of 100) The dependent variable for your analysis is Final mark. Answer the following questions using dataset 1. (a) Estimate a regression model using X to predict Y (state the simple linear regression equation). (b) Interpret the meaning of the slope. (c) Predict Y when X = 26. (d) Compute the coefficient of determination and interpret its meaning. (e) Compute the standard error of the estimate and interpret its meaning. Judge the magnitude of the standard error of the estimate. (f) Perform a residual analysis (plot the residuals) and evaluate whether the assumptions of regression have been violated. (g) Test for the slope using t test (follow all the necessary steps). Assume 5% level of significance. (h) Test for the slope using F test (follow all the necessary steps). Assume 5% level of significance. (i) Test for the correlation coefficient (follow all the necessary steps). Assume 5% level of significance. (j) Compute a 95% confidence interval estimate of the mean Y for all students when X = 26 and interpret its meaning. (k) Compute a 95% prediction interval of Y for an individual student when X = 26 and interpret its meaning. 1 ECON7300: Statistical Project Assignment, Semester 2, 2016 Instructions for Dataset 4: Multiple Regression Analysis (45 marks) Life insurance companies are keenly interested in predicting how long their customers will live, because their premiums and profit-ability depend on such numbers. A statistician for one insurance company gathered data from 100 recently deceased male customers. He recorded the age at death of the customer, ages at death of his mother and father, and whether the man was a smoker. The variables in the dataset are:  Longevity (Y, age at death of the male customer)  Mother (X1, age at death of his mother)  Father (X2, age at death of his father)  Smoker (X3, coded 1 if the man was a smoker, and 0 if the man was not a smoker) The dependent variable for your analysis is Longevity. Answer the following questions using dataset 4. (a) Estimate a regression model using X1 and X2 to predict Y (state the multiple regression equation). (b) Interpret the meaning of the slopes. (c) Predict Y when X1 = 72 and X2 = 65. (d) Compute a 95% confidence interval estimate of the mean Y for all male customers when X1 = 72 and X2 = 65 and interpret its meaning. (e) Compute a 95% prediction interval of Y for a male customer when X1 = 72 and X2 = 65 and interpret its meaning. (f) Plot the residuals to test the assumptions of the regression model. Is there any evidence of violation of the regression assumptions? Explain (g) Determine the variance inflation factor (VIF) for each independent variable (X1 and X2) in the model. Is there reason to suspect the existence of collinearity? (h) At the 0.05 level of significance, determine whether each independent variable (X1 and X2) makes a significant contribution to the regression model (use t tests and follow all the necessary steps). On the basis of these results, indicate the independent variables to include in the model. (i) Test for the significance of the overall multiple regression model at 5% level of significance. 2 ECON7300: Statistical Project Assignment, Semester 2, 2016 (j) Determine whether there is a significant relationship between Y and each independent variable (X1 and X2) at the 5% level of significance (hint: testing portions of the multiple regression model using the partial F test). (k) Compute the coefficients of partial determination and interpret their meaning (l) Estimate a regression model using X1, X2 and X3 to predict Y (state the multiple regression equation, the regression equation for smoker, the regression equation for non-smoker) and interpret the coefficient for X3. (m) Estimate a regression model using X1, X2, X3, an interaction between X1 and X2, an interaction between X1 and X3, and an interaction between X2 and X3 to predict Y. (n) Test whether the three interactions significantly improve the regression model. Assume 5% level of significance (hint: test the joint significance of the three interaction terms using the partial F test. If you reject the null hypothesis, test the contribution of each interaction separately (using the partial F test) in order to determine which interaction terms to include in the model). 3 SUMMARY OUTPUT Regression Statistics Multiple R 0.834386 R Square 0.6962 Adjusted R Square 0.692968 Standard Error 8.645672 Observations 96 Residuals 40 df SS MS F Significance F 1 16101.68 16101.68 215.4139 4.7E-26 94 7026.279 74.74765 95 23127.96 Coefficients Standard Error t Stat Intercept 25.51259 3.574654 7.13708 X Variable 1 1.750642 0.119278 14.67698 RESIDUAL OUTPUT ObservationPredicted Y Residuals 1 78.03187 -7.03187 2 34.26581 -4.26581 3 88.53572 -6.53572 4 90.28636 7.713638 5 81.53315 -3.53315 6 65.77737 7.222631 7 85.03444 -3.03444 8 85.03444 8.965565 9 100.7902 -1.79022 10 85.03444 -0.03444 11 81.53315 -7.53315 12 78.03187 0.968134 13 88.53572 -6.53572 14 95.53829 -7.53829 15 67.52801 -12.528 16 69.27865 -7.27865 17 76.28122 14.71878 18 62.27608 3.723916 19 79.78251 6.217492 20 78.03187 -5.03187 21 83.28379 6.716207 22 78.03187 9.968134 23 83.28379 7.716207 24 64.02673 -0.02673 25 76.28122 6.718777 26 67.52801 19.47199 27 78.03187 17.96813 28 79.78251 4.217492 29 83.28379 8.716207 30 69.27865 12.72135 0 -20 ANOVA Regression Residual Total 20 P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 1.97E-10 18.41503 32.61015 18.41503 32.61015 4.7E-26 1.513813 1.987472 1.513813 1.987472 0 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 92.037 71.0293 76.28122 95.53829 85.03444 86.78508 76.28122 90.28636 86.78508 76.28122 97.28893 88.53572 83.28379 97.28893 74.53058 72.77994 74.53058 79.78251 69.27865 74.53058 43.01902 69.27865 69.27865 79.78251 50.02159 93.78765 74.53058 78.03187 72.77994 58.7748 69.27865 88.53572 79.78251 39.51773 88.53572 69.27865 64.02673 83.28379 81.53315 50.02159 99.03957 78.03187 78.03187 65.77737 55.27351 85.03444 72.77994 76.28122 71.0293 69.27865 76.28122 44.76966 83.28379 90.28636 76.28122 -4.037 3.970704 3.718777 -1.53829 7.965565 7.214922 19.71878 -9.28636 -9.78508 -6.28122 -5.28893 -13.5357 -1.28379 -8.28893 7.469419 -12.7799 -3.53058 -0.78251 -12.2787 0.469419 1.980982 -6.27865 3.721346 15.21749 -13.0216 1.212353 1.469419 12.96813 4.220062 -7.7748 -14.2787 -1.53572 -1.78251 -6.51773 4.46428 19.72135 -14.0267 -4.28379 5.46685 -0.02159 -18.0396 -10.0319 -1.03187 1.222631 -3.27351 8.965565 -2.77994 -5.28122 -6.0293 -16.2787 0.718777 10.23034 9.716207 -7.28636 0.718777 86 87 88 89 90 91 92 93 94 95 96 74.53058 57.02416 57.02416 81.53315 86.78508 88.53572 83.28379 76.28122 79.78251 85.03444 53.52287 -3.53058 10.97584 -13.0242 8.46685 0.214922 -3.53572 12.71621 -10.2812 3.217492 0.965565 -1.52287 X Variable 1 Residual Plot 40 20 0 -20 0 10 20X Variable 30 1 40 50 Sheet1 Study time Final mark 30 71 5 30 36 82 37 98 32 78 23 73 34 82 34 94 43 99 34 85 32 74 30 79 36 82 40 88 24 55 25 62 29 91 21 66 31 86 30 73 33 90 30 88 33 91 22 64 29 83 24 87 30 96 31 84 33 92 25 82 38 88 26 75 29 80 40 94 34 93 35 94 29 96 37 81 35 77 29 70 41 92 36 75 33 82 41 89 28 82 27 60 28 71 31 79 25 57 28 75 10 45 Page 5 Sheet1 25 25 31 14 39 28 30 27 19 25 36 31 8 36 25 22 33 32 14 42 30 30 23 17 34 27 29 26 25 29 11 33 37 29 28 18 18 32 35 36 33 29 31 34 16 63 73 95 37 95 76 91 77 51 55 87 78 33 93 89 50 79 87 50 81 68 77 67 52 94 70 71 65 53 77 55 93 83 77 71 68 44 90 87 85 96 66 83 86 52 Page 6 Longevity Mother Father Smoker 80 85 78 0 73 88 63 1 70 66 75 1 72 72 67 1 79 88 73 0 83 90 72 0 70 67 65 1 72 76 71 1 72 66 75 1 71 78 64 1 67 69 66 1 74 71 76 0 80 74 77 0 63 68 66 1 71 70 70 1 66 64 66 1 74 82 71 0 71 71 71 1 65 75 60 1 74 76 66 0 66 69 68 1 71 76 67 1 73 69 80 1 74 79 70 0 68 74 62 1 77 81 78 0 77 85 69 0 74 77 69 1 68 72 71 1 68 75 63 1 74 82 66 0 71 73 72 1 80 84 73 0 72 75 61 1 77 82 76 0 76 88 69 0 62 65 57 1 70 75 57 1 71 72 67 1 69 72 63 1 73 79 71 1 72 77 69 1 84 80 90 0 73 76 74 1 70 78 70 1 78 75 74 0 82 77 67 72 67 72 75 72 75 80 72 71 71 89 74 72 74 77 77 73 72 65 81 76 64 72 69 59 69 76 63 66 72 68 73 78 83 78 67 70 68 66 75 71 72 71 77 83 75 68 69 67 78 73 71 73 84 78 76 77 86 79 72 78 85 72 67 74 66 82 80 71 73 75 59 73 82 71 74 85 72 80 82 82 82 73 77 74 80 76 71 77 76 79 78 66 69 72 67 64 69 66 73 75 64 61 70 77 71 77 68 77 72 71 64 63 77 70 67 69 67 62 69 65 56 64 60 66 75 72 82 70 62 60 79 63 72 60 64 67 74 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 67 68 67 74 70 72 69 68 71 76 77 66 78 73 68 61 62 64 68 70 60 1 1 1 0 1 1 1 ...
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Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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