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Published byMeryl Evans Modified over 4 years ago

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Correlation & Regression – Non Linear Emphasis Section 3.3

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Non Linear Regression Shapes…… Positive Quadratic Regression: Negative Quadratic Regression:

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Non Linear Regression Shapes…… Positive Exponential Regression: Negative Exponential Regression:

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Quadratic and Exponential on Calculator…… Quadratic: Exponential:

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What should you look for to tell if it is not linear?...... Sometimes a high “r” value for linear regression is deceptive. You must look at the scatter plot AND you must look at the residual pattern it makes. Residuals – positive and negative deviations from the least squares line. Each residual is the difference between the observed y value and the corresponding predicted y value. If the residuals have a curved pattern then it is NOT linear.

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Example……The scatter plot could possibly be linear. You must check the residual pattern. xy 516.3 109.7 158.1 204.2 451.9 253.4 601.3

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Change y-list to resids after running a linear correlation regression – 2 nd stat resid: Notice the curved pattern in the residuals. It is either quadratic or exponential.

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This is a quadratic regression….. Equation:

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Example 2……Is it linear? xy 01 -30.125 -40.0625 38 416 532

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Look at the residuals…… There is a curved pattern in the residuals. It is NOT linear – we will see that it is exponential. (Positive)

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Here is the equation you should use for predictions:

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Practice Assignment…… Worksheet

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