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O’Brien ISOM 201 Fall 2023 ISOM 201 Final Exam December 14 th , 2023 Problem 1. (10 Marks) The following regression is trying to predict, murders per annum per 1,000,000 inhabitants. Using the variables number of inhabitants, percent with incomes below $5000 and percent unemployed. SUMMARY OUTPUT Regression Statistics Multiple R 0.904609234 R Square 0.818317866 Adjusted R Square 0.784252466 Standard Error 4.589778444 Observations 20 ANOVA df SS MS F Significance F Regression 3 1518.144941 506.0483 24.02197 3.62889E-06 Residual 16 337.0570587 21.06607 Total 19 1855.202 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% ower 95.0% Upper 95.0% Intercept -36.76492528 7.010925772 -5.24395 8.03E-05 -51.62742398 -21.9024 -51.6274 -21.9024 Inhabitants 7.62937E-07 6.36301E-07 1.199019 0.247978 -5.85961E-07 2.11E-06 -5.9E-07 2.11E-06 Percent with incomes below $5000 1.192174211 0.561653909 2.122614 0.049741 0.001521112 2.382827 0.001521 2.382827 Percent unemployed 4.719821372 1.530475467 3.083892 0.007116 1.475358319 7.964284 1.475358 7.964284 Answer. A. What is the coefficient of determination? What is its value? (1 Mark) - The coefficient of determination is the R Square which measures the explanatory power of a regression model that takes into consideration the number of independent variables in the model. It is 0.8183 which means in other words, the independent variables explain 81.83% of the variance on the dependent variables. B. Is this a linear model? Why? (2 Marks) - This is a linear model because the adjusted R Square value is high. This is an indication of linearity. On the ANOVA table the regression model is significant, (F-statistic = 24.02197, p-value = 3.62889E-06). This means that the relationship Page 1 of 4

O’Brien ISOM 201 Fall 2023 between the independent variables and the dependent variable is likely to be due to something more than chance. C. What are the independent variables? Are each of them adding value to the equation? Explain why. (3 Marks) - The independent variables are inhabitants, percent with income below 5000, and percent unemployed. Inhabitants is not adding value to the equation because the p-value is not significant at 0.24, which is above 0.05. Percent with income below 5000, and percent unemployed have p-values of 0.049, and 0.007, which are both below 0.05. Therefore, percent with income below 5000, and percent unemployed are both significant. D. Define the regression equation. (2 Marks) - The regression equation: - Murders per annum per 1,000,000 inhabitants = -36.764925 + 7.62937e-07 * Number of inhabitants + 1.192174 * Percent with incomes below $5000 + 4.719821 * Percent unemployed E. If a community has 800,000, 15% of incomes are below $5000 and unemployment is 10%. What is the prediction for murders per year, for 1,000,000 people? (2 Marks) - Murders per annum per 1,000,000 inhabitants = -36.764925 + 7.62937E-07 *800,000 + 1.192174 * 15 + 4.719821 * 10 = 15.57 Therefore, there would be 15.57 murders per year per 1,000,000 people in this community. Page 2 of 4

O’Brien ISOM 201 Fall 2023 Problem 2. (10 Marks) Using the table below creating a 3-year and 4-year moving average and predict sales for 2008. Find the mean absolute deviation (MAD) for both the 3 and 4 year moving averages.( MAD = Σ | Error | n Answer. Year Sales 3-Year Moving Average Absolute Error 3-year Moving Average 4-Year Moving Average Absolute Error 4-Year Moving Average 2001 2030 2002 2155 2003 2382 2004 2412 (2030+2155+2382)/3 = 2189 (2412-2189) =223 2005 2606 (2155+2382+2412)/3 = 2316.33 (2606- 2316.33) = 289.667 (2030+2155+2382+ 2412)/4 = 2244.75 (2606- 2244.75) = 361.25 2006 2892 (2382+2412+2606)/3 = 2466.667 (2892- 2466.667) = 425.33 (2155+2382+ 2412+2606)/4 = 2388.75 (2892- 2388.75) = 503.25 2007 3018 (2412+2606+2892)/3 = 2636.667 (3018- 2636.667) = 381.33 (2382+ 2412+2606+2892)/4 = 2573 (3018-2573) = 445 2008 MAD 3-Year Moving Average = Σ | Error | n error= 223+289.667+425.33+381.33 = 1319.327 = 1319.327/4 = 329.83 Page 3 of 4

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O’Brien ISOM 201 Fall 2023 MAD 4-Year Moving Average = Σ | Error | N error= 361.25+503.25+445 = 1309.5 = 1309.5/3 = 436.5 Page 4 of 4

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