invest_3ed.pdf

# G different choices of explanatory variable the

• 429
• 60% (5) 3 out of 5 people found this document helpful

This preview shows pages 373–376. Sign up to view the full content.

be and is most useful for comparing different models (e.g., different choices of explanatory variable). The coefficient of determination is equal to the square of the correlation coefficient and so is denoted by r 2 or R 2 (and is often pronounced “r - squared.”)

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

Chance/Rossman, 2015 ISCAM III Investigation 5.8 373 Another measure of the quality of the fit is s , the standard deviation of the residuals. This is a measure of the unexplained variability about the regression line and gives us an idea of how accurate our predictions should be (the actual response should be within 2 s of the predicted response). If s is much smaller than the variability in the response variable ( s y ) then we have explained a good amount of variability in y . Most statistical packages report s , or it can be found from ) 2 /( ± n SSE . (cc) Determine and interpret the value of s for these data. [What are the units?] Study Conclusions There is a fairly strong positive linear association between the foot length of statistics students and their heights ( r = 0.711). To predict heights from foot lengths, the least-squares regression line is foot eight h 03 . 1 3 . 38 ˆ ² . This indicates that if one person’s foot length measurement is one centimeter longer than another, we will predict that person’s height to be 1.03 inches taller. This regression line has a coefficient of determination of 50.6%, indicating that 50.6% of the variability in heights is explained by this least squares regression line with foot length. The other 49.4% of the variability in heights is explained by other factors (perhaps including gender) and also by natural variation. So although the foot lengths are informative, they will not allow us to perfectly predict the heights of the students in this sample. The value of s is 3.61 inches, meaning we should be able to predict a person’s height within 3.61 inches based only on the size of his or her foot. Technology Detour Determining Least Squares Regression Lines In R To calculate intercept and slope: > lm(response~explanatory) To then superimpose regression line on scatterplot: > abline(lm(response~explanatory)) In Minitab x Choose Stat > Regression > Regression > Fit Regression Model and specify the response variable in the first box and then the explanatory variable in the Predictors box. x To superimpose the regression line on the scatterplot, choose Stat > Regression > Fitted Line Plot . x Minitab reports additional output, but you should be able to find the least-squares regression equation and the value of r 2 . x Click the Storage button and check the Residuals box to store them in their own column.
Chance/Rossman, 2015 ISCAM III Investigation 5.8 374 Practice Problem 5.8 For the Cat Jumping data set from Investigation 5.6: (a) Calculate and interpret the correlation coefficient between velocity and body mass. (b) Square the correlation coefficient to obtain r 2 . Interpret the coefficient of determination in context.

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

This is the end of the preview. Sign up to access the rest of the document.
• Spring '14
• -STAFF

{[ 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