ECON 3300 LEC

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ECON 3300 LEC 13

• 11/06/06

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Multiple regression

• Several explanatory variables are used to predict
  independent variable

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Example OmniPower bar sales
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Example OmniPower bar sales
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Multiple Regression

• Regression coefficients net regression
  coefficients
• Net regression coefficients Average change in Y
  per unit change in a particular X, holding
  constant effect of other X variables.

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Coefficient of Multiple Determination

• Proportion of variation in Y that is explained by
  the set of explanatory variables (two or more)
  selected.

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Coefficient of Multiple Determination
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• OmniPower example
• SSR39472730.77
• SST52093677.44

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Residual Analysis

• Residual plots used in multiple regression

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Residual Analysis
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Significance of linear relationship

• Hypothesis testing of whether ß1(population
  slope) is equal to zero - determines if
  significant linear relationship exists between
  the X and Y variables
• Ho ß1 ß2 ßk0
• Ha At least one ßj?0
• Rejection of Null hypothesis Evidence of linear
  relationship

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F Test for Slope
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F Test for Slope

• Rejection rule
• FcalcgtFa,k,n-k-1 - Reject H0

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t Test for Slope

• t Test statistic can be used to make this
  conclusion

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Confidence Interval Estimate of Slope

• Alternative way of testing existence of linear
  relationship
• If the interval does not contain zero the
  regression coefficient ßj has a significant
  effect.