solutions11 - ISDS Homework 11 Solutions...

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Unformatted text preview: ISDS Homework 11 - Solutions Regression & Interval Estimates Panayiotis Skordi 1. A scatter diagram includes the following points: x 4 3 5 2 1 6 y 11 7 10 7 5 15 Two regression models are proposed: y = 3 + 2x y = 2 + 3x Using the least squares method, find the regression model providing a better fit to the data. ANSWER Using the least squares method, find the regression model providing a better fit to the data. x y xy x 2 y 2 4 11 44 16 121 3 7 21 9 49 5 10 50 25 100 2 7 14 4 49 1 5 5 1 25 6 15 90 36 225 count x y xy x 2 y 2 6 21 55 224 91 569 1 -- = 2 2 ) ( ) ( ) )( ( ) ( x x n y x xy n m 2 ) 21 ( ) 91 ( 6 ) 55 )( 21 ( ) 224 ( 6-- = 105 189 = 8 . 1 = n x m y b - = ) ( 6 ) 21 ( 8 . 1 55- = 87 . 2 = The regression line for this example would be: y = 1.8x + 2.87 from y = mx + b ALTERNATIVELY USE x y x y 2 3 + = x y 3 2 + = ( 29 2 2 3 y x- + ( 29 2 3 2 y x- + 4 11 11 14 9 3 7 9 11 4 16 5 10 13 17 9 49 2 7 7 8 1 1 5 5 5 6 15 15 20 25 count squares method 13 100 First equation has a smaller sum of squares error, therefore would be a better fit, according to the least 2 2 ) ( y y - 2 ) ( y y - 2. The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last months sales (in $1,000s) and the years experience of 10 randomly selected salespeople. The data gathered are listed below: Salesperson Years of Experience Sales 1 7 2 2 9 3 10 20 4 3 15 5 8 18 6 5 14 7 12 20 8 7 17 9 20 30 10 15 25 a) Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate. b) Determine the least squares regression line. c) Interpret the value of the slope of the regression line. d) Estimate the monthly sales of a salesperson with 16 years of experience. ANSWERS 3 b. x y xy x 2 y 2 7 49 2 9 18 4 81 10 20 200 100 400 3 15 45 9 225 8 18 144 64 324 5 14 70 25 196 12 20 240 144 400 7 17 119 49 289 20 30 600 400 900 15 25 375 225 625 count x y xy x 2 y 2 10 82 175 1811 1020 3489 c) Interpret the value of the slope of the regression line For each additional year of experience, monthly sales of a salesperson increase by an average of $1,081.7. d) Estimate the monthly sales of a salesperson with 16 years of experience. when x = 16 63 . 8 0817 . 1 + = x y ( 29 94 . 25 63 . 8 16 0817 . 1 = + = 4 -- = 2 2 ) ( ) ( ) )( ( ) ( x x n y x xy n m 2 ) 82 ( ) 1020 ( 10 ) 175 )( 82 ( ) 1811 ( 10-- = 3476 3760 = 0817 . 1 = n x m y b - = ) ( 10 ) 82 ( 0817 . 1 175- = 6299 . 8 = The regression line for this example would be: y = 1.0817x + 8.63 from y = mx + b 3. Given the least squares regression line x y 63 . 1 48 . 2 +- = , and a coefficient of determination of 0.81, find the coefficient of correlation....
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solutions11 - ISDS Homework 11 Solutions...

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