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Ch. 12 The Regression Line

Ch. 12 The Regression Line. Slope and intercept: y -intercept: point where x =0 slope = r*SDy/SDx Regression equation: y =slope* x + y -intercept The regression equation can be used to make a prediction of y when x is given. . Example #3 from Activity: The Regression Line

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Ch. 12 The Regression Line

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

  2. Example #3 from Activity: The Regression Line • Calculate the slope • Write the equation in point-slope form: y- (average y) = slope(x – (average x)) • Solve to find the y-intercept • Predict the mpg if weight=4000 lbs. • Graph the regression line.

  3. Definition of a regression line: • Data could 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. • The y-intercept is a theoretical construct which is not always meaningful.

  4. The slope is always meaningful, as seen in the (*) questions in the activity. • Activity: The Regression Line • Work on #1, 2, 4 in pairs.

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