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H-SC MATH 121 - Lecture 42 - Calculating the Regression Line

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Homework ReviewFormulas for the Regression LineThe Regression Line on the TI-83Interpolation and ExtrapolationFree Lunch vs. Graduation RateAssignmentCalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentCalculating the Regression LineLecture 42Section 13.3.2Robb T. KoetherHampden-Sydney CollegeTue, Apr 7, 2009CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentOutline1Homework Review2Formulas for the Regression Line3The Regression Line on the TI-834Interpolation and Extrapolation5Free Lunch vs. Graduation Rate6AssignmentCalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentHomework ReviewExercise 13.2, page 821.Data were gathered to estimate the regression line for amodel where a gymnast’s score (y) depends on thegymnast’s physical condition as measured by his or herweight (x).The estimated regression line is given byˆy = 1190 − 1.9x.Complete the following sentence:Every additional pound that a gymnast weighs dropsthe predicted score by about ______ points, onaverage.CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentHomework ReviewExercise 13.2, page 821.The slope −1.9 tells how fast ˆy changes with respect tox.That is, the slope represents the change in ˆy for anincrease of 1 in x.Therefore, if a gymnast gains one pound, then weexpect his score to drop by 1.9 points.CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineThe equation of the regression line is of the formˆy = a + bx.b is the slope of the regression line.a is the y-intercept.We need to find the coefficients a and b from the data.CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineThe formula for b isb =P(x − x)(y − y)P(x − x)2The formula for a isa = y − bx.CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineExample (Strong Positive Association)++++++++++--+++++CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineExample (Weak Positive Association)---+++++++--+++-+CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineExample (Strong Negative Association)--+------+ -------CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineExample (Weak Negative Association)----++---+ --+---+CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentThe Least Squares Regression LineAn alternate formula for b isb =nPxy −PxPynPx2− (Px)2.This is the one that the TI-83 uses.CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Consider again the data setx y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 83 124 95 148 169 2011 1715 24CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Compute the x deviations.x y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 8 -63 12 -44 9 -35 14 -28 16 19 20 211 17 415 24 8CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Compute the y deviations.x y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 8 -6 -73 12 -4 -34 9 -3 -65 14 -2 -18 16 1 19 20 2 511 17 4 215 24 8 9CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Compute the squared x deviations.x y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 8 -6 -7 363 12 -4 -3 164 9 -3 -6 95 14 -2 -1 48 16 1 1 19 20 2 5 411 17 4 2 1615 24 8 9 64CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Compute the squared y deviations.x y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 8 -6 -7 36 493 12 -4 -3 16 94 9 -3 -6 9 365 14 -2 -1 4 18 16 1 1 1 19 20 2 5 4 2511 17 4 2 16 415 24 8 9 64 81CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Compute the product of x and y deviations.x y x − x y − y (x − x)2(y − y)2(x − x)(y − y)1 8 -6 -7 36 49 423 12 -4 -3 16 9 124 9 -3 -6 9 36 185 14 -2 -1 4 1 28 16 1 1 1 1 19 20 2 5 4 25 1011 17 4 2 16 4 815 24 8 9 64 81 72CalculatingtheRegressionLineRobb T.KoetherHomeworkReviewFormulas fortheRegressionLineTheRegressionLine on theTI-83InterpolationandExtrapolationFree Lunchvs.GraduationRateAssignmentExampleExample (Calculating the Regression Line)Find


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H-SC MATH 121 - Lecture 42 - Calculating the Regression Line

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