Lecture22.pdf - ECON10005 Quantitative Methods 1 Lecture 22...

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ECON10005 Quantitative Methods 1 Lecture 22 1
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Regression of house price on house size Population regression model: E ( Price Size ) = β + β Size i i 0 1 i Sample regression model: Price = 10.724 + 12.651 Size i i ^ R = 0.633 2 2
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Population : E ( Price Size ) = β + β Size i i 0 1 i Statistical Inference for Regression Coefficients Regression results may be presented in equation form: = 10.724 + 12.651 Size n = 15, R = 0.633 Price ^ i i 2 (2.671) (49.180) Or in table form: Variable Intercept Size Coefficient 10.724 12.651 S.E. 49.180 4 2.671 t -stat 0.218 4.737 p -value 0.8308 0.0004 n = 15, R = 0.633 2 3
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Population : E ( Price Size ) = β + β Size i i 0 1 i Statistical Inference for Regression Coefficients Regression results may be presented in equation form: = 10.724 + 12.651 Size n = 15, R = 0.633 Price ^ i i 2 (2.671) (49.180) Or in table form: Variable Intercept Size Coefficient 10.724 12.651 S.E. 49.180 4 2.671 t -stat 0.218 4.737 p -value 0.8308 0.0004 n = 15, R = 0.633 2 t -statistics for H : β = 0 and 0 0 H : β = 0 0 1 4
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Population : E ( Price Size ) = β + β Size i i 0 1 i Statistical Inference for Regression Coefficients Regression results may be presented in equation form: = 10.724 + 12.651 Size n = 15, R = 0.633 Price ^ i i 2 (2.671) (49.180) Or in table form: Variable Intercept Size Coefficient 10.724 12.651 S.E. 49.180 4 2.671 t -stat 0.218 4.737 p -value 0.8308 0.0004 n = 15, R = 0.633 2 Two tail p -values 5
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Population : E ( Y X ) = β + β X i i 0 1 i Statistical Inference for the Conditional Mean ( Y X ) = + X E ^ i i β ^ 0 β ^ 1 i Sample: For a given number x , we estimate E ( Y X = x ) = β + β x i i 0 1 using ( Y X = x ) = + x E ^ i i β ^ 0 β ^ 1 Example. The estimated average price for 21sq. houses: ( Price Size = 21) = 10.724 + 12.651 × 21 = 254.954 E ^ i i What is the s.e. for this estimate? Compute a confidence interval?
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