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Unformatted text preview: 1 Regression The probability theorist wants to sell his house. So, he wants to estimate the expected price. He found some historic data about houses sold recently in his area. The data are shown in the following table. 2 Regression house 1 2 3 4 5 6 Area, x 1000 sq.ft. 1.8 2.1 2.3 3.0 3.4 3.6 Price, x 1000$ 202 243 251 289 341 374 3 Regression Assuming there is a linear relationship between the house size and its price, find the estimate of its parameters. The PTs house is 2800 sq.ft. Find the estimated expected price and 95% confidence intervals on the expected price and the actual sale price. A P + = 1 4 Regression The linear relation is usually not exact. A realistic model is: Where and 1 are regression coefficients. i i i x Y + + = 1 5 Random Error Properties of distribution A mean of zero Symmetry around zero An assignment of greater probability to small errors than to larger ones Errors are assumed to be: Independent Have same variance ( homoscedasticity ) i 6 Method of Least Squares Consider the simple formula: Where the random errors are independent samples from N(0, ) How to find the estimators of and 1 ? + + = x Y 1 7 Least Squares Estimates Need an index to measure discrepancy between points and line Focus on vertical disparities between...
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This note was uploaded on 03/17/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .
 Spring '08
 Perevalov

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