AP Statistics Section 15 B

Estimating the Parameters

To estimate the true regression line , we will use the calculated least-squares

regression line . The y-intercept, a, will be an unbiased estimator of the true y-intercept, , and the slope, b, is an unbiased estimator of

the true slope, .

xy

bxay ˆ

The remaining parameter of the model is the standard deviation, , which describes the variability of the response y about the true regression line. We will estimate the unknown standard deviation by a

sample standard deviation of the residuals (i.e. the standard error about the least-squares line)

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The slope, , of the true regression line is usually the most important parameter in a regression problem. The confidence

interval for has the familiar form: estimate . Because b is our estimate, the confidence interval becomes __________. In this expression, the standard error of the least-squares slope b

is

and t* is the critical value for the t(n – 2) density curve with area C between –t* and t*.

estimateSEt

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Example: Construct and interpret a 95% confidence interval for the slope of the true regression line for the crying baby/IQ scenario.

The population of interest is __________

Conditions:

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Example: Construct and interpret a 95% confidence interval for the slope of the true regression line for the

crying baby/IQ scenario.

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The figure below shows the basic output for the crying study from the regression command in the Minitab software package. Regression AnalysisThe regression equation isIQ = 91.3 + 1.49 Crycount Predictor Coef StDev T PConstant 91.268 8.934 10.22 0.000Crycount 1.4929 0.4870 3.07 0.004 S = 17.50

bSEStatistic

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Estimates