O'Reilly logo

Statistical Inference: A Short Course by Michael J. Panik

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

12.3 Estimating the Slope and Intercept of the Population Regression Line

Let us develop the following notation. The population regression line will be written as

(12.4) equation

and the sample regression line will appear as

(12.5) equation

where img is the sample estimate of img and img is the sample estimate of img. The sample regression line is illustrated in Fig. 12.4. Note that there are two values of Y that occur at each Xi value—the observed value of Y or Yi, and the estimated value of Y or img. Their difference, img, will be termed the ith residual or ith deviation from the sample regression line. This residual is “observed” and serves as an estimate of εi, which is purely random and thus “unobserved.”

Figure 12.4 The ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required