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# F1 - King Fahd University of Petroleum and Minerals

F1 - King Fahd University of Petroleum and Minerals

STAT 212 Business Statistics II 2 1. (32 marks = 5+3+3+9+6+2+1+3) Can demographic information be helpful in predicting sales at sporting goods stores? The monthly sales totals are recorded for a sample of 38 stores in a large chain of nationwide sporting goods stores. For each of the 38 stores, eight variables are recorded, namely; Sales (Y): Latest one-month sales total (\$). Age (X1): Median age of customers (years). HS (X2): Percentage of customers with high school diploma. College (X3): Number of customers with college diploma. Growth (X4): Annual population growth rate of customers over the past ten years (%). Income (X5): Median family income of customers (\$). Location of store: ⎧ X6 = 1 if located in Down Town & 0 otherwise. ⎪ ⎨X7 = 1 if located in Urban Area & 0 otherwise. ⎪ ⎩ Default location = Rural Area. For the following output, answer the questions that follow: Regression Analysis: Y versus X1; X2; X3; X4; X5; X6; X7 The regression equation is Y =60636 + 9132 X1 + 9084X2 + 13.34 X3 - 3594 X4 + 5949 X5 + 2014681 X6 + 696342 X7 Predictor Coef SE Coef T P VIF Constant 60636 1805584 I 0.973 X1 9132 44818 0.20 0.840 1.334 X2 9084 21166 0.43 0.671 1.445 X3 13.34 II 0.90 0.373 3.856 X4 -3594 18024 -0.20 0.843 4.047 X5 5949 13923 0.43 0.672 2.879 X6 III 198295.374 10.16 0.000 1.953 X7 696342 173976 4.00 0.0004 1.720 S = 407009 R-Sq = 83.7% R-Sq(adj) = 79.9% Analysis of Variance Source DF SS MS F P Regression 7 2.55192093E+13 3.64501329E+12 22.05 0.000 Residual Error 30 4.96969070E+12 1.656562567E+11 Total 37 3.04889000E+13 Predicted Values for New Observations New Obs Fit SE Fit 99% CI 99% PI 1 1785588 1298290 ( IV ; 5355880) ( V ; 5526920) Values of Predictors for New Observations New Obs X1 X2 X3 X4 X5 X6 X7 1 30.0 1.00 29000 31.0 79.0 0.000000 1.00 a. Write down below the quantities that should be in the boxes labeled I-V in the MINITAB output above. I_____________ II_____________ III_____________ IV______________ V_______________ b. What is the slope of the Number of customers with college diploma? Interpret it. Slope = - Interpret:______________________________________________________ ___________________________________________________________________________________

STAT 212 Business Statistics II 3 c. Is there any potential multicolinearity problem with this regression analysis? Explain your answer with appropriate details from the MINITAB output. A potential multicollinearity exists Yes / No (circle one) Explanation: d. Is the overall model statistically significant at the 0.05 level? H 0 : The test hypotheses are: H A : The test statistic value = The critical value(s) = Reject H 0 if The decision rule is: The decision is: Conclusion is: We have (enough/not enough) _____________evidence that _______ ________________________________________________________ e. Is the Median family income significantly linearly related to Sales? Explain. H 0 : The test hypotheses are: H A : The test statistic value = Reject H 0 if The decision rule is: The decision is: f. Write the regression model for stores located in the Down Town area. Model: - g. With Age=30, HS =1, College =29000, Growth = 31, Income =75, and a store located at an urban area, what is the fitted Sales value? Fitted value = h. Find 99% C.I. for the regression coefficient of Growth, and interpret this C.I. A 99% C.I. for the regression coefficient of Growth is Interpretation

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F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum & Minerals
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F1 - King Fahd University of Petroleum & Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum & Minerals
F1 - King Fahd University of Petroleum & Minerals
F1 - King Fahd University of Petroleum and Minerals
F1 - King Fahd University of Petroleum and Minerals
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E1 - King Fahd University of Petroleum and Minerals
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