Chapter8rev

Chapter8rev - Chapters8 LinearRegression...

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Chapters 8 Linear Regression
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At the end of this chapter, you  should be able to Calculate a regression line given summary  statistics. Interpret the slope and intercept of the  regression line. Find predictions and residuals for points. Interpret a residual plot. Interpret the R 2  value for a regression. Understand the limitations of regression.
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Correlation and Regression Correlation = linear relationship  between two variables. Summarize relationship with line. Called Regression line. Explanatory variable ( x ) Response variable ( y )
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Regression line Explains how response variable ( y changes in relation to explanatory  variable ( x ). Use line to predict value of  y  for given  value of  x .
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Regression line Need mathematical formula. Different lines by sight. Predict  y  from  x . The predicted values are called   . Values on the regression line. The observed values are called  y . Points in the scatterplot. y ˆ
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Regression line Look at vertical distance Error  in regression line. Place line to make these errors as small  as possible. y y e ˆ - =
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Least squares regression (LSRL) Most commonly used regression line. Puts line where sum of the squared  errors as small as possible. Minimizes  Based on statistics r s s y x y x , , , , 2 e
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Regression line equation where x b b y 1 0 ˆ + = x y s s r b = 1 x b y b 1 0 - =
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Regression line equation b 1  = slope of line.   For every unit increase in  x ,    changes by  the amount of the slope. Very important for interpreting data. b 0  =  y -intercept of line.   The value of    when  x  = 0. Usually not important for interpreting data. Values of  x  are usually not close to 0. y ˆ y ˆ
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Calculating the regression  line. Degree Days vs. Gas Usage 9953 . 0 , 37 . 3 , 74 . 17 , 31 . 5 , 31 . 22 = = = = = r s s y x y x x y s s r b = 1
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Calculating the regression  line. Degree Days vs. Gas Usage 9953 . 0 , 37 . 3 , 74 . 17 , 31 . 5 , 31 . 22 = = = = = r s s y x y x 19 . 0 74 . 17 37 . 3 ) 9953 . 0 ( 1 = = = x y s s r b
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Calculating the regression  line. Degree Days vs. Gas Usage 9953 . 0 , 37 . 3 , 74 . 17 , 31 . 5 , 31 . 22 = = = = = r s s y x y x 19 . 0 74 . 17 37 . 3 ) 9953 . 0 ( 1 = = = x y s s r b x b y b 1 0 - =
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Calculating the regression  line. Degree Days vs. Gas Usage 9953 . 0 , 37 . 3 , 74 . 17 , 31 . 5 , 31 . 22 = = = = = r s s y x y x 19 . 0 74 . 17 37 . 3 ) 9953 . 0 ( 1 = = = x y s s r b 07 . 1 ) 31 . 22 ( 19 . 0 31 . 5 1 0 = - = - = x b y b
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line. Don’t forget to write the equation.
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Chapter8rev - Chapters8 LinearRegression...

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