Lecture22

Lecture22 - STAT 350 Lecture 22 Chapter 3.3 Least Square...

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STAT 350 Lecture 22 Chapter 3.3 Least Square Regression Line

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3.3 Fitting a Line (Regression line) If X and Y has a linear relationship: Find the line which best fits the data Regression Line Use this line to predict Y for given values of X Recall: Equation of straight line: y = a + b x
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 population, compared to their father’s height Galton developed Regression Analysis to study this effect, which he called “regression toward mediocrity”.

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Illustration of Least Square Regression Line
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 vertical 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! x y 696 . 0 53 . 61 ˆ
Finding the Least Squares Regression Line The solution gives:

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Alternate calculations Meaning of slope b: How much does Y change if X is changed by 1 unit ? ( Rise over run ) Directly related to the correlation x y s s r b
Find the equation for the regression line. Summary statistics are given:

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Lecture22 - STAT 350 Lecture 22 Chapter 3.3 Least Square...

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