Chapter 11--Regression and Correlation Methods

# testing the hypothesis h0 j 0 vs ha j 0 the null

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Unformatted text preview: n Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables Inference about Individual Partial Slopes Cont’d... Testing the hypothesis H0 : βj = 0 vs Ha : βj = 0. The null hypothesis means xj has no additional (unique) prediction value given the other x s. The test statistic, ˆ βj t= . ˆˆ SE (βj ) We reject H0 when |t | ≥ t1−α/2,n−(k +1) . One sided tests can be done in the usual way. A 100(1 − α)% conﬁdence interval for βj is ˆ ˆˆ βj ± t1−α/2,n−(k +1) SE (βj ). Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables An Example: Determinants of House Price Data on the following variables were collected for 51 homes on the market in the University neighborhood of Missoula in 2001. Variable Price: Age: Bed: Bath: Size: Lot: The The The The The The Description price of the home thousands of dollars age of the home in years number of bedrooms number of bathrooms interior area of the home in thousands of square feet size of the lot in thousands of square feet Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction Least Square Estimates of the Parameters Inference about the Parameters Prediction Assessing Adequacy of Fit Correlation Multiple Regression Introduction Inferences in Multiple Regression Tests for Subset of Regression Coeﬃcients Prediction (Forecasting) Dummy Variables An Example: Determinants of House Price Cont’d... The ANOVA Table, Source Regression Residual Total SS 65843.737 13626.106 7...
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