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Lecture23 - STAT350 Lecture22 Chapter3.3...

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STAT 350 Lecture 22 Chapter 3.3 Least Square Regression Line
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3.3 Fi<ng a Line (Regression line) If X and Y has a linear relaEonship: Find the line which best fits the data Regression Line Use this line to predict Y for given values of X Recall: EquaEon of straight line: y = a + b x
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Historical Note on Regression Line Sir Francis Galton discovered a phenomenon called Regression Toward the Mean Taller fathers tended to have somewhat shorter sons, and vice versa Son’s height tended to regress toward the mean height of the populaEon, compared to their father’s height Galton developed Regression Analysis to study this effect, which he called “regression toward mediocrity”.
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IllustraEon of Least Square Regression Line
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Example 40 45 50 55 60 65 70 155 160 165 170 175 180
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Least Squares Regression Line Regression line is: How do we know this is the right line? What makes it best? It is the Least Squares Regression Line It is the line which makes the verEcal distances from the data points to the line as small as possible Uses the concept of sums of squares Small sums of squares is good Least Squares!
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Finding the Least Squares Regression Line The soluEon gives:
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Alternate calculaEons Meaning of slope b: How much does Y change if X is changed by 1 unit ? ( Rise over run ) Directly related to the correlaEon
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Example 3.7 on page 117 Find the equaEon for the regression line.
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