Example (Ch.11 Set D #3 p.193) In order to use the normal approximation, the scatter diagram should be football-shaped with points thickly scattered in the center and fading at the edges. If a scatter diagram is football-shaped, take the points in a narrow vertical strip and they will be away from the regression line by amounts similar to the RMS(error). –The new average is estimated from the regression method –The new SD is approximately equal to the RMS(error) of the regression line. Example set E #1 p. 197

Ch. 12 The Regression Line Slope and intercept: –y-intercept: point where x=0 –slope = –Regression equation: y=slope*x + y-intercept The regression equation can be used to make a prediction of y when x is given.

Definition of a regression line: –Data can be summarized by many lines. What is special about the regression line is that it has the smallest RMS(error). This is referred to as Least Squares. Interpretation: –Extrapolating beyond the data is questionable, at best. Examples: 1.Lost baggage situation: We could not compare executive jets to major commercial airlines based on only major airline data. 2.Height vs. weight for adult males: Could not make predictions about height or weight of children based on adult data. 3.Education level: If data only goes up to 16 years of education, we could not make predictions for those with 20 years of education based on the data.

–The y-intercept is a theoretical construct which is not always meaningful. –The slope is always meaningful – represents the rate of change. Example #3 from Activity: The Regression Line 1.Calculate the slope 2.Write the equation in point-slope form: y- (average y) = slope(x – (average x)) 3.Solve to find the y-intercept 4.Predict the mpg if weight=4000 lbs. 5.Graph the regression line.

Activity: The Regression Line –Work on #1, 2, 4 in pairs.