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Chapter 8 Notes

Chapter 8 Notes. A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. Regression (unlike correlation) requires we have an explanatory & response variable. The least square reg. line.

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Chapter 8 Notes

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  1. Chapter 8 Notes

  2. A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. • Regression (unlike correlation) requires we have an explanatory & response variable.

  3. The least square reg. line • The least-squares regression line (LSRL) is a mathematical model for the data. • The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

  4. Equation: With slope: And intercept: *We write (“y hat”) in the equation of the regression line to emphasize that the line gives a predicted response y for any x.

  5. We only use these formulas when we do not have the data itself.

  6. When we write a least squares regression equation we do not use x & y, we use the variable names themselves… • For example: • Predicted score = 52 + 1.5(hours studied)

  7. Coefficient of Determination • The coefficient of determination, r2, is the fraction of the variation in the value of y that is explained by least-squares regression of y on x. • When we explain r2then we say… ___% of the variability in ___(y) can be explained by the linear regression of ___(y) on ___(x).

  8. Residuals • A residual is the difference between an observed value of the response variable and the value predicted by the regression line. That is, Residual = observed y – predicted y or Residual = y – • The mean of the residuals is always zero.

  9. A residual plot plots the residuals on the vertical axis against the explanatory variables on the horizontal axis. • Such a plot magnifies the residuals and makes patterns easier to see. • A residual plotshow good linear fit when the points are randomly scattered about y = 0 with no obvious patterns.

  10. To create a residual plot on the calculator: • 1)You must have done a linear regression with the data you wish to use. • 2) From the Stat-Plot, Plot # menu choose scatterplot and leave the x list with the x values. • 3) Change the y-list to “RESID” chosen from the list menu. • 4) Zoom – 9

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