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Unformatted text preview: University of California, Davis ARE 106 - Winter 2011 Homework 2 The quiz based on these homework problems will be held at the beginning of class on Thursday, January 20, 2011 Computational Questions 1. Recall the example I gave in class about how the size of a house, measured in square feet, might influence the value of the house, measured in thousands of dollars. I went to Yahoo! Real Estate (http://realestate.yahoo.com/California/Davis) and found the following sample data on home size and home price for seven homes currently for sale in Davis. Home Price ($ 000’s) Home Size (sq. ft.) Address 584 1811 1312 Redwood 299 1148 4322 Cowell 770 2504 1119 Pistachio 335 942 719 Kestrel 379 2233 1504 Baywood 910 3867 3927 Hoopa 525 1594 514 Reed (a) First, write down the econometric model implied by this example, identifying the dependent ( y ) and explanatory ( x ) variables. The econometric model is y i = β 1 + β 2 x i + e i where y i is home price and x i is home size. (b) Plot each point on graph paper or using a spreadsheet program such as Microsoft Excel. Make sure to clearly label your graph, putting the explanatory variable on the x-axis and the dependent variable on the y-axis. There is a table attached to the end of this assignment. Filling out each cell in this table will help you answer the remaining questions. (c) Calculate the sample mean for both home price and home size. Estimate the variance of y using ˆ σ 2 y = ∑ n i =1 ( y i- ¯ y ) 2 n- 1 . The table gives you the values for y and x. Filling in each cell gives you the things that go into the formulas for sample means and sample variances. You can refer to the table to find the answers. To estimate the variance of y, take each value in the column for ( y i- ¯ y ), square it, sum up all of the values and divide by n- 1. 1 University of California, Davis ARE 106 - Winter 2011 ( y- ¯ y ) 2 1669.306 59605.735 51464.163 43323.449 26942.878 134584.163 329.163 317918.857 To find the variance: 317918 . 857 /n- 1 = 317918 . 857 / 6 = 52986 . 476 (d) Calculate ∑ 7 i =1 ( x i- ¯ x ) 2 and ∑ 7 i =1 ( x i- ¯ x )( y i- ¯ y ). See the table. (e) Estimate the covariance of home price and home size. Do you expect it to be positive or negative? We would expect the covariance to be positive because we expect bigger houses to have higher prices. Recall the covariance is ∑ ( x i- ¯ x )( y i- ¯ y ) f ( x i ,y i ). For a sample covariance, we can replace f ( x i ,y i ) with (1 /n- 1). From the table, taking ∑ ( x i- ¯ x )( y i- ¯ y ) and dividing by n = 7 gives a covariance of 198146.98. (f) Employing your answers from above, calculate the least squares estimates, b 1 and b 2 , for the parameters of your econometric model....
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This note was uploaded on 01/13/2012 for the course ARE 32482 taught by Professor Havenner during the Spring '10 term at UC Davis.
- Spring '10