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Ch04_43-47

# Ch04_43-47 - 72106 CH04 GGS 2:05 PM Page 43 C H A P T E R...

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43 T EACHING S UGGESTIONS Teaching Suggestion 4.1: Which Is the Independent Variable? We fnd that students are oFten conFused about which variable is independent and which is dependent in a regression model. ±or example, in Triple A’s problem, clariFy which variable is X and which is Y . Emphasize that the dependent variable ( Y ) is what we are trying to predict based on the value oF the independent ( X ) variable. Use examples such as the time required to drive to a store and the distance traveled, the totals number oF units sold and the selling price oF a product, and the cost oF a computer and the processor speed. Teaching Suggestion 4.2: Statistical Correlation Does Not Always Mean Causality. Students should understand that a high R 2 doesn’t always mean one variable will be a good predictor oF the other. Explain that skirt lengths and stock market prices may be correlated, but rais- ing one doesn’t necessarily mean the other will go up or down. An interesting study indicated that, over a 10-year period, the salaries oF college proFessors were highly correlated to the dollar sales vol- ume oF alcoholic beverages (both were actually correlated with in²ation). Teaching Suggestion 4.3: Give students a set oF data and have them plot the data and manually draw a line through the data. A discussion oF which line is “best” can help them appreciate the least squares criterion. Teaching Suggestion 4.4: Select some randomly generated values For X and Y (you can use random numbers From the random number table in Chapter 15 or use the RAND Function in Excel). Develop a regression line using Excel and discuss the coeFfcient oF determination and the ±-test. Students will see that a regression line can always be developed, but it may not necessarily be useFul. Teaching Suggestion 4.5: A discussion oF the long Formulas and short-cut Formulas that are provided in the appendix is helpFul. The long Formulas provide students with a better understanding oF the meaning oF the SSE and SST. Since many people use computers For regression problems, it helps to see the original Formulas. The short-cut Formulas are helpFul iF students are perForming the computations on a calculator. A LTERNATIVE E XAMPLES Alternative Example 4.1: The sales manager oF a large apart- ment rental complex Feels the demand For apartments may be related to the number oF newspaper ads placed during the previous month. She has collected the data shown in the accompanying table. Ads purchased, (X) Apartments leased, (Y) 15 6 94 40 16 20 6 25 13 25 9 15 10 35 16 We can fnd a mathematical equation by using the least squares regression approach. Leases, Y Ads, X ( X 2 ¯¯ X ) 2 ( X 2 ¯¯ X )( Y 2 ¯¯ Y ) 61 5 6 4 3 2 4 9 196 84 16 40 289 102 62 0 9 1 2 13 25 4 6 92 5 4 2 2 10 15 64 0 16 35 144 72 o Y 5 80 o X 5 184 o ( X 2 ¯¯ X ) 2 5 774 o ( X 2 ¯¯ X )( Y 2 ¯¯ Y ) 5 306 b 1 5 306/774 5 0.395 b 0 5 10 2 0.395(23) 5 0.915 The estimated regression equation is ˆ Y 5 0.915 1 0.395 X or Apartments leased 5 0.915 1 0.395 ads placed IF the number oF ads is 30, we can estimate the number oF apart- ments leased with the regression equation 0.915 1 0.395(30) 5 12.76 or 13 apartments

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