Homework6_Solutions - ISOM 111 L7-L8, Fall 2010 1 Homework...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 4

Homework6_Solutions - ISOM 111 L7-L8, Fall 2010 1 Homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online