10.2-10.3

10.2-10.3 - STAT3000 Section 10.2 10.3 Inference about...

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STAT3000 Section 10.2 – 10.3: Recall finding a predicted value: Ex) In a study to determine how the skill level in doing a complex job is influenced by the amount of training, 15 new recruits were given varying amounts of training (from 2 to 12 hours). After the training, their times to perform the job were recorded. The least squares linear regression line is ˆ y = 37.86 – 1.702x. The predicted value of y for x = 10 hours is closest to? Yhat=37.86-1.702 (10) =20.84 ( average at predicted value a. 36.16 b. 37.86 c. 20.84 d. 10.58 e. None of the above. 209

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Step 4: When satisfied with the model, use the model to estimate the expected value of y and to predict a future value of y. The most common uses of a regression model are: 1) estimating the mean value of y, E(y), for a specific value of x and 2) predicting a new individual y value for a specific value of x y = β 0 + β 1 x + ε E(y) = β 0 + β 1 x 0 1 ˆ y b b x = + ˆ y is both the estimator 210
The difference between these two model uses lies in the relative accuracy of the estimate and the prediction. At x = x * for ˆ y the estimator , * 2 ˆ 1 ( ) xx x x SE n SS μ σ - = + At x = x * for ˆ y the predictor, * 2 ˆ 1 ( ) 1 y xx x x SE n SS - = + + 211

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α )% CI for E(y) at x = x * : * 2 1 ( ) ˆ * xx x x y t s n SS - ± + where t* is based on n-2 degrees of freedom. A 100(1- α )% PI for y at x = x * : * 2 1 ( ) ˆ * 1 xx x x y t s n SS - ± + + where t* is based on n-2 degrees of freedom. Using the least squares prediction equation to estimate the mean value of y or to predict a particular value of y for values of x that fall outside the range of the values of x contained in the sample data may lead to errors that are much larger than expected. 212
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10.2-10.3 - STAT3000 Section 10.2 10.3 Inference about...

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