Section2.4posted_1

# Section2.4posted_1 - ST OR 155 Section 2 T uesday Febr uar...

This preview shows pages 1–9. Sign up to view the full content.

STOR 155, Section 2 Tuesday, February 2, 2010 Section 2.4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Section 2.4: Cautions about correlation and regression Residuals Outliers and influential observations Lurking variables Correlations based on averaged data Restricted-range problem (omitted)
Residuals In a regression, there are three numbers connected with every individual: x, the value of the explanatory variable, y, the observed value of the response variable, and ŷ , the predicted value of the response variable. The observed and predicted values y and ŷ are almost never equal. The difference y – ŷ is called the residual for that individual (or for that x ). residual for a value x in the dataset = y – ŷ.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
x = parent s’ averag e height y = daughte r’s height = ŷ predicte d daughte r’s height resid ual 63.5 60 61.90 - 1.90 67.0 66 65.27 + 0.73 65.5 65 63.83 + 1.17 69.5 66 67.68 - 1.68 67.5 67 65.75 + 1.25 65.5 63 63.82 - 0.82 70.0 69 68.16 + 0.84 63.0 63 61.42 + 1.58 63.0 61 61.42 - 0.42 67.5 65 65.75 - 0.75 Residuals: Example Parents’ heights as predictor of daughter’s height for n = 10 women. Regression line is For x = 63.5 : 61.90 = 0.69 + 0.96 63.5. Residual for first x is y – ŷ = 60 – 61.90 = −1.90. ŷ = 0.69 + 0.96 x
For x = 63.5 : 61.90 = 0.69 + 0.96 63.5. Residual for first x is y – ŷ = 60 – 61.90 = −1.90. Residuals The residuals are the vertical distances that regression wants to minimize.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Residuals The residuals appear as vertical distances on the plot of the regression line. Or, we can plot them by themselves. Why would we want to plot them by themselves?
Residual plots r 2 is high and the fit looks good in the scatterplot. But the residual plot does a better job of showing that the fit is much better for values of x near the center than at the two ends. Scatterplot and regression Residual plot (Ex. 2.20, p. 128 shows this also.)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outliers and influential observations Earlier we saw the effect that outliers can have on the correlation .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern