Chapter 05 - Chapter 5 Regression Essential Statistics...

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Essential Statistics Chapter 5 1 Chapter 5 Regression
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Essential Statistics Chapter 5 2 Objective : To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects with a given value of the explanatory variable. Linear Regression
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Essential Statistics Chapter 5 3 Prediction via Regression Line Number of new birds and Percent returning Example : predicting number (y) of new adult birds that join the colony based on the percent (x) of adult birds that return to the colony from the previous year.
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Essential Statistics Chapter 5 4 Least Squares Used to determine the “best” line We want the line to be as close as possible to the data points in the vertical ( y ) direction (since that is what we are trying to predict) Least Squares : use the line that minimizes the sum of the squares of the vertical distances of the data points from the line
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Essential Statistics Chapter 5 5 Least Squares Regression Line Regression equation: y = a + bx ^ x is the value of the explanatory variable y-hat is the average value of the response variable (predicted response for a value of x) note that a and b are just the intercept and slope of a straight line note that r and b are not the same thing, but their signs will agree
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Chapter 5 6 Prediction via Regression Line Number of new birds and Percent returning The regression equation is y-hat = 31.9343 - 0.3040 x y-hat is the average number of new birds for all colonies with percent x returning For all colonies with 60% returning, we predict the average number of new birds to be 13.69: 31.9343 - (0.3040)( 60 ) = 13.69 birds Suppose we know that an individual colony has
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Chapter 05 - Chapter 5 Regression Essential Statistics...

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