chapter11 - CHAPTER 11: INFERENCE FOR REGRESSION 11.1...

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1 CHAPTER 11: INFERENCE FOR REGRESSION 11.1 Estimated Regression Line ? Sales Price Sq. Footage N e t I n c o m e Price Sales Family net income Sq. Footage of home
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2 Suppose there is a linear relationship between two quantitative variables X and Y and the values y i of Y are given at x 1 , x 2 ..x n . X x 1 x 2 x 3 .... x n Y y 1 y 2 y 3 .... y n Y X Predict the value of Y at any value x of X. Y X
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3 The least-squares regression line ˆ Ya b X =+ makes the sum of squares of the vertical deviations of the data points from the line as small as possible. Y ˆ Y Residual = observed Y – predicted Y = Y- ˆ . Y Example: Footage vs. Income X = family net income (in thousands of dollars), Y = square footage (in hundreds of square feet), A random sample of n=10 families from a neighborhood: X 22 26 45 37 28 50 56 34 60 40 Y 16 17 26 24 22 21 32 18 30 20 predicted ˆ Y observed Y residual ˆ YY
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4 Scatterplot of Footage vs. Income INCOME 70 60 50 40 30 20 FOOTAGE 40 30 20 10 8.514 0.354 . Footag eI n c o m e =+⋅ The values of a = 8.514 and b = 0.354 were calculated from the sample data. The intercept a and the slope b would take different values if another sample of 10 families were obtained. The population of all families from the neighborhood The random sample of 10 families used to obtain the least-squares regression line
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5 11.2 Inferences in Regression Let X, Y be two quantitative variables, X Y.
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chapter11 - CHAPTER 11: INFERENCE FOR REGRESSION 11.1...

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