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Understanding Linear Regression Analysis & Techniques

Linear regression is an analytic method to establish the connection between variables. Learn about lines of best fit, extrapolation, interpolation, least squares fit, residuals, and practical usage on TI-89 and TI-83/84 calculators. Evaluate outlier effects and complete the assignment.

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Understanding Linear Regression Analysis & Techniques

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  1. 3.2 Linear Regression

  2. Regression • Is an analytic technique for determining the relationship between a dependent and an independent variable.

  3. Interpolating/Extrapolation • Once we develop a line of best fit we can estimate point beyond the available data • This is process is called extrapolation or interpolation

  4. How are lines of best fit created? • How?

  5. Least Squares Fit • Residual • The sum of the residuals is zero • The sum of the area of the squares created by the residuals is the least possible value

  6. Ti-89 • Enter data into data/matric area as usual. • Hit F5 “calc” • Select “linreg” and fill in data as we talked about yesterday. • Go into “Y=” part of calc. • There you should see your line of best fit. • To see your plotted points hit the up button. • Select “plot1” • Make the entries as follows: “scatter” “box”, c1,c2. Then hit enter twice. • Go to the graph portion of Calc and you should see it. • If you can’t see info, zoom out.

  7. Ti-83/84 • Enter data in stat edit area. • Perform LinReg as yesterday. • Record “a” value and “b” value. • Hit “y=” • Type in “y=ax+b” except replace “a” and “b” with value you found. • Hit enter. Not hit 2nd “y=”. • Turn on plot 1. • Go to graph area.

  8. Effects of Outliers • To evaluate the performance of one of its instructors, a driving school tabulates the number of hours of instruction and the driving-test scores for the instructors students

  9. Effect of Outliers • What assumption is the management of the driving school making? Is the assumption reasonable? • Analyze these data to determine whether they suggest that the instructor is an effective teacher. • Comment on any data that seem unusual. • Determine the effect of any outliers.

  10. Assignment • Pg 180 #’s 1-3,5-7

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