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22/08/2022
Can demographic information be helpful in predicting sales at sporting goods stores? The data at left are monthly sales totals from a random sample of 38 stores in a large chain of nationwide sporting goods stores. All stores in the franchise, and thus within the sample, are approximately the same size and carry the same merchandise. The county, or in some cases counties, in which the store draws the majority of its customers is referred to here as the customer base. For each of the 38 stores, demographic information about the customer base is provided. The variables in the data set are:
Sales – Latest one month sales total (dollars)
Age – Median age of customer base (years)
HS – Percentage of customer base with a high school diploma
College – Percentage of customer base with a college diploma
Growth – Annual population growth rate of customer base over the past 10 years.
Income – Median family income of customer base (dollars)
Q-2a. Construct a scatter plot, using sales as the dependent variable and median family income as the independent variable. Discuss the scatter plot.
Q-2b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
Q-2c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem.
Q-2d. Compute the coefficient of determination r2, and interpret its meaning.
Q-2e. Construct a 95% confidence interval estimate of the population slope and interpret its meaning.
Sales Age Growth Income Sales HS College 1695712.62 33.16 0.8299 26748.51 $1,695,712.62 73.5949 17.8350 3403862.053 32.67 0.6619 53063.79 $3,403,862.05 88.4557 31.9439 2710352.905 35.66 0.9688 36090.14 $2,710,352.91 73.5362 18.6198 529215.459 33.07 0.0821 32058.07 $ 529,215.46 79.1780 20.6284 663686.654 35.76 0.4646 47843.42 $ 663,686.65 84.1838 35.2032 2546324.335 33.81 2.1796 50180.97 $2,546,324.34 93.4996 41.7057 2787046.202 30.98 1.8048 30710.08 $2,787,046.20 78.0234 28.0250 612696.054 30.78 -0.0569 29141.7 $ 612,696.05 70.2949 15.0882 891822.033 32.32 -0.1577 25980.15 $ 891,822.03 70.6674 10.9829 1124967.965 32.53 0.3664 18730.88 $1,124,967.97 63.7395 13.2458 909500.976 31.44 2.2256 31109.23 $ 909,500.98 76.9059 19.5500 2631166.881 33.16 1.5158 35614.12 $2,631,166.88 82.9452 20.8135 882972.654 31.87 0.1413 23038.43 $ 882,972.65 65.2127 16.9796 1078573.124 33.41 -1.0400 34531.72 $1,078,573.12 73.4944 32.9920 844320.194 34.05 1.6836 30350.36 $ 844,320.19 80.2201 22.3185 1849119.029 28.89 2.3596 38964.94 $1,849,119.03 87.5973 24.5670 3860007.316 36.11 0.7840 49392.77 $3,860,007.32 85.3041 30.8790 826573.88 32.81 0.1164 25595.69 $ 826,573.88 65.5884 17.4545 604682.868 33.05 1.1498 29622.61 $ 604,682.87 80.6176 18.6356 1903611.6 33.50 0.0606 31586.1 $1,903,611.60 80.3790 38.3249 2356808.391 32.68 1.6338 39674.56 $2,356,808.39 79.8526 23.7780 2788571.957 28.52 1.1256 28878.98 $2,788,571.96 81.2371 16.9300 634878.286 32.89 1.4884 24287.08 $ 634,878.29 70.2244 19.1429 2371627.369 30.50 4.7937 46711.24 $2,371,627.37 87.1046 30.8843 2627837.961 30.29 1.8922 33449.81 $2,627,837.96 80.2057 26.5570 1868116.33 31.29 1.8667 31694.45 $1,868,116.33 75.2914 28.3600 2236796.862 33.05 1.7896 25459.22 $2,236,796.86 77.6162 19.2490 1318876.234 32.93 0.2707 47047.34 $1,318,876.23 85.1753 35.4994 1868097.836 31.84 3.0129 26433.24 $1,868,097.84 74.1792 18.6375 1695218.566 31.08 23.4630 33396.66 $1,695,218.57 81.6991 41.1130 2700194.415 32.18 0.7041 26179.36 $2,700,194.42 73.4140 17.8566 1156049.774 31.69 -0.1569 33454.64 $1,156,049.77 73.7161 26.5426 643858.444 34.03 0.7084 42271.5 $ 643,858.44 78.6493 29.8734 2188687.363 34.73 0.1353 46514.75 $2,188,687.36 80.9503 24.5374 830351.94 30.56 0.3848 27030.81 $ 830,351.94 66.8057 14.1390 1226905.572 33.52 0.7417 42910.08 $1,226,905.57 77.8905 20.8340 566903.589 32.40 0.6693 40561.4 $ 566,903.59 79.3622 19.0309 826518.398 29.91 0.1111 22325.96 $ 826,518.40 58.3610 10.6729
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