PPT5.5 Addendum to Simple Linear Regression

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Adding a Quadratic Term to a SLR Sometimes a straight will not adequately express the relationship between a response variable Y and an independent variable X. In such a case it may be necessary to add a quadratic term to the regression equation.

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Example of quadratic equation Consider the following data:
Selecting the Fitted Line Plot Option in Minitab

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Linear Fit vs Quadratic Fit Linear Plot: R 2 = 0.0% Quadratic Plot: R 2 = 80.6%
Creating the X 2 variable using the CALC menu in Minitab

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Minitab Worksheet with XSquare Variable
Including the quadratic term in the model R 2

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Conclusion We note that both x and x 2 terms are significant (p=0.001) so that both should be retained in the model. In this example, the linear model Y = β 0 + β 1 X is not a useful model for predicting Y values, whereas the

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Unformatted text preview: quadratic model Y = + 1 X + 2 X 2 is a highly significant model that explains over 80% of variability in Y . Use of Transformations Consider the following data set relating Salary to Years of Experience The full data set consists of 50 values. SLR of Salary (Y) on Experience (X) Residual Plot exhibits heteroscedasticity Define the new variable lnY SLR of ln Y vs X Heteroscedasticity is not evident Exponential relationship between Y and X The log-linear equation ln Y = 9.84 + 0.05 X can easily be transformed to the exponential equation Y = e 9.84+0.05X = e 9.84 e 0.05x =18769e 0.05X showing that Y is an exponential function of X. Conclusion Heteroscedasticity may be reduced or eliminated by taking a transformation of the dependent variable. Logarithmic and square root transformations are commonly used....
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