Homework6_Solutions

# Homework6_Solutions - ISOM 111 L7-L8 Fall 2010 1 Homework 6...

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Unformatted text preview: ISOM 111 L7-L8, Fall 2010 1 Homework 6 Solutions I . A real estate agency collects data concerning y = the sales price of a house (in thousands of dollars), and x = the home size (in hundreds of square feet). The data are given in the following table. Sales Price ( y ) 180 98.1 173.1 136.5 141 165.9 193.5 127.8 163.5 172.5 Home Size ( x ) 23 11 20 17 15 21 24 13 19 25 (a). By using the formulas illustrated in Lecture 20, verify the least squares estimates b = 48 . 02 , b 1 = 5 . 70 . (b). Interpret the meanings of b and b 1 . Does the interpretation of b make practical sense? (c). Write the least squares estimation/prediction equation. (d). Use the least squares line to obtain a point estimate of the mean sales price of all houses having 2,100 square feet and a point prediction of the sales price of an individual house having 2,100 square feet. (e). When the least squares line is fit to the 10 observations, we obtain SSE = 896 . 8 . Calculate s 2 and s . (f). Find the correlation coefficient r of x and y based on the data. Solution : (a) Based on the data provided, n = 10 , X x i = 188 , X y i = 1551 . 9 , X x 2 i = 3736 , X x i y i = 30324 . 9 . Hence SXY = X x i y i- ( ∑ x i )( ∑ y i ) n = 30324 . 9- 188 × 1551 . 9 10 = 1149 . 18 , SXX = X x 2 i- ( ∑ x i ) 2 n = 3736- 188 2 10 = 201 . 6 , and b 1 = SXY SXX = 1149 . 18 201 . 6 = 5 . 70 , b = ¯ y- b 1 ¯ x = 1551 . 9 10- 5 . 70 × 188 10 = 48 . 02 . (b) b 1 (= 5 . 70) (thousand dollars) is the estimated increase in mean sales price of houses for every one hundred square feet increase in the home size. b (= 48 . 02) is the estimated mean sales price of houses when home size = 0; this interpretation does not make practical sense....
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Homework6_Solutions - ISOM 111 L7-L8 Fall 2010 1 Homework 6...

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