Chapter 11--Regression and Correlation Methods

# Chapter 11 regression and correlation methods stat

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Unformatted text preview: 1,1 , xn+1,2 , . . . , xn+1,k new values on the k predictor variables. The expected value of y for the new values of the predictor variables is estimated by, ˆˆ ˆ ˆ µ y |x ˆ = β0 +β1 xn+1,1 +β2 xn+1,2 +· · ·+βk xn+1,k . ,x ,...,x n+1 n+1,1 n+1,2 n+1,k The same quantity is used to estimate yn+1 . The diﬀerence is in the standard errors and, hence, the conﬁdence and prediction intervals are given, respectively, by ˆµ µ y |x ˆ ±t1−α/2,n−(k +1) SE (ˆy |x ,x ,...,x ,x ,...,x n+1 n+1,1 n+1,2 n+1 n+1,k n+1,1 ˆy and yn+1 ± t1−α/2,n−(k +1) SE (ˆn+1 ). ˆ Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics n+1,2 n+1,k ) 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 For the house price data, using only Bedroom and Size as predictors, estimate the price of a brand new house that is with 1390 square feet interior area. The ﬁtted regression equation µPrice|Bed,Size = 30.148 − 11.657Bed + 61.543Size. ˆ The 95% conﬁdence interval for the expected price is from \$74, 088 to \$86, 987. The 95% prediction interval for the price is from \$44, 294 to \$116, 780. 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 Extrapolation In simple linear regression (when there is only one independent variable) extrapolation occurs when we try to predict y or µy |x for a value of x well beyond the range of the data. In multiple regression, extrapolation depends not only on the range of each separate xj predictor but also on the correlation among the x s. When making predictions (forecasts) we must consider not only whether each independent variable is reasonable but also wh...
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