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Estimating the ParametersTo 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, .
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)
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 isand t* is the critical value for the t(n – 2) density curve with area C between –t* and t*.
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:
.025 .95 Example: Construct and interpret a 95% confidence interval for the slope of the true regression line for the crying baby/IQ scenario.
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 CrycountPredictorCoefStDev T PConstant 91.268 8.934 10.22 0.000Crycount 1.4929 0.4870 3.07 0.004S = 17.50
