lecture_2_3

lecture_2_3 - Looking at data relationships Least-squares...

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    Looking at data: relationships   Least-squares regression IPS chapter 2.3 © 2006 W. H. Freeman and Company
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Objectives (IPS chapter 2.3) Least-squares regression The regression line Making predictions: interpolation Coefficient of determination, r 2
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x y 0144 . 00080 . 0 ˆ + =
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Correlation tells us about strength (scatter) and direction of the linear relationship between two quantitative variables. In addition, we would like to have a numerical description of how both variables vary together. For instance, is one variable increasing faster than the other one? And we would like to make predictions based on that numerical description. But which line best describes our data?
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Distances between the points and line are squared so all are positive values. This is done so that distances can be properly added. The regression line The least-squares regression line is the unique line such that the sum of the squared vertical ( y ) distances between the data points and the line is the smallest possible.
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Properties is the predicted y value (y hat) b is the slope a is the y -intercept ˆ y "a" is in units of y "b" is in units of y / units of x The least-squares regression line can be shown to have this equation: bx a y x s s r x s s r y y x y x y + = + - = ˆ or , ) ( ˆ
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b = r s y s x First we calculate the slope of the line, b ; from statistics we already know: r is the correlation. s
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lecture_2_3 - Looking at data relationships Least-squares...

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