QM670RegressionExample

# QM670RegressionExample - Regression Example Or More Fun...

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Regression Example Or “More Fun Than a Barrel of Typical Values”

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Note: Refer to the “QM 670 Regression Problems” Handout Failure to do so could cause symptoms such as headaches, confusion, or drowsiness Please do not operate heavy machinery while doing QM homework
Plot of Price vs. Square Footage Price vs. Square Footage 0 100 200 300 400 500 0 1000 2000 3000 4000 5000 Square feet Price (in \$000)

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Description Positive Linear Two high leverage observations (Sq. Feet = \$2,900, \$3,900)
Regression Output (from Excel) SUMMARY OUTPUT Regression Statistics Multiple R 0.877138 R Square 0.769371 Adjusted R Square 0.756558 Standard Error 43.3346 Observations 20

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Regression Output (Cont.) ANOVA df SS MS F Significance F Regression 1 112762.2 112762.2 60.04739 3.84707E-07 Residual 18 33801.97 1877.887 Total 19 146564.2 Coefficients Standard Error t Stat P-value Intercept -133.679 38.53064 -3.46942 0.002736 Sq.Feet 0.136086 0.017562 7.749025 3.85E-07
Description of Output Part 1: Regression Equation Regression Equation: Y(hat) = -133.679 + 0.136086X

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Slope Slope (b 1 ) = 0.136086 This means that for each additional square foot, the price will increase by \$136. (Remember, prices are in thousands of dollars.)
Intercept Y-intercept (b 0 ) = -133.679 This means that the predicted price of a house with zero square feet is -\$133,679. Since there are no houses with zero square feet (even in Hong Kong or New York), this estimate is not very meaningful.

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Extrapolation Prediction of this type is known as “extrapolation.” This occurs when we predict y for x-values outside of the range as those in our sample. Here, our x-values ranged between 1,300 and 3,900 square feet. While we sometimes need to extrapolate (especially in forecasting), we are less confident in our predictions when we do.
Goodness of Fit The correlation coefficient (R) = .877138 This indicates a strong positive linear relationship between price and square footage. The coefficient of determination (R2) = . 769371

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Continued The coefficient of determination (R2) = . 769371 This means that 76.9% of the variation in price is explained using square footage as an explanatory variable. (The remaining 23.1% of variation remains unexplained. Perhaps we should add a variable?)
Continued The adjusted R2 is 0.756558 The standard error is 43.3346 While these are nice and quaint, they are not overly useful in simple linear regression. But in multiple regression,…

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ANOVA Output Here, we are testing to see if square footage is a useful linear predictor of price. The p-value (Significance F) is 0.000000385, or in computerese, 3.85E-07. (This is scientific notation, and it means 3.85X10^-7.) We compare the p-value to our preset level of significance.
Unless otherwise specified, we will set our level of significance (denoted by α) at 0.05. If our p- value is less than α, we conclude that there is a useful linear relationship. Here, the p-value (0.000000385) is less than

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## This note was uploaded on 12/02/2011 for the course QM 670 taught by Professor Dr.keeney during the Fall '11 term at Jefferson College.

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QM670RegressionExample - Regression Example Or More Fun...

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