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,.
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 is and 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.. 95. 025
The figure below shows the basic output for the crying study from the regression command in the Minitab software package. Regression Analysis The regression equation is IQ = 91.3 + 1.49 Crycount PredictorCoefStDevTP Constant91.2688.93410.220.000 Crycount1.49290.48703.070.004 S = 17.50