HW 10 Req HW Solutions - Chap 12

HW 10 Req HW Solutions - Chap 12 - Problem Solutions for...

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Problem Solutions for Required Homework #10 from Chapter 12 12.4. Given n = 5 sample data for percent women employees and percent women managers. Let x denote the independent variable of the percent women employees and let y denote the dependent variable of the percent women managers. % women employees % women management 67 49 45 21 73 65 54 47 61 33 a. Graph of the n = 5 sample data. 0 10 20 30 40 50 60 70 40 45 50 55 60 65 70 75 % Working % Management b. There appears to be an increasing linear relationship between the percentage of women working in the five companies ( x ) the ASW 5e Req HW #10 from Chap 12 1 © Harvey Singer
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percentage of management jobs held by women in that company ( y ). The trend is increasing, meaning that y generally increases as x increases. Therefore, anticipate that the slope b 1 of the line will be positive. c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y . But there’s only one “best” fitting line. In part (d) we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Calculations: calcs height (in, x) weight (lbs, y) x^2 x*y y^2 67 49 4489 3283 2401 45 21 2025 945 441 73 65 5329 4745 4225 54 47 2916 2538 2209 61 33 3721 2013 1089 sums 300.00 215.00 18480.00 13524.00 10365.00 means 60.00 43.00 The calculation summary is: n = 5 xbar = 60.00 ybar = 43.00 Σ x 2 = 18480.00 Σ xy = 13524.00 Σ y 2 = 10365.00 Substituting these results into the operational equations for slope and y-intercept, the calculated regression parameters are ASW 5e Req HW #10 from Chap 12 2 © Harvey Singer
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( ) ( ) ( ) 35 - 78 - 43 60 30 . 1 - 43 x b - y b 30 . 1 480 624 18000 - 18480 12900 - 13524 60 5 - 18480 43 60 5 - 13524 x n - x y x n - xy b 1 0 2 2 2 1 = = × = = = = = × × × = = The results are: b 1 = 1.30 (slope) b 0 = -35.00 (y-intercept) The regression equation is Y = 1.30x – 35.00 where Y is the percent of management jobs expected to be held by women for x percent of women employees. Note: Interpretation of b 1 : The units on b 1 are % woman managers/% woman employees. The sign is positive, meaning that the % woman managers is expected to increase with increasing % woman employees. ASW 5e Req HW #10 from Chap 12 3 © Harvey Singer
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As an average rate, for each and every one percent increase percent of women employees, the percent of management jobs expected to be held by woman will increase by 1.30%. Note: In the calculation of b 1 , num b 1 = 624 den b 1 = 480 _________________________________________________________ Before proceeding to part e for a prediction, look at the correlation analysis below to answer whether the linear association between the variables is strong enough for the regression equation to be used as a predictive tool. Calculate the coefficients of correlation (r) and of determination
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This note was uploaded on 02/19/2011 for the course OM 210 taught by Professor Singer during the Spring '08 term at George Mason.

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HW 10 Req HW Solutions - Chap 12 - Problem Solutions for...

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