Regression with Microsoft Excel 2007

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TWO-VARIABLE LINEAR REGRESSION

The population regression model is: y = β₁ + β₂ x + u

We wish to estimate the regression line: y = b₁ + b₂ x

REGRESSION USING THE DATA ANALYSIS ADD-IN

This requires the Data Analysis Add-in: see Excel 2007 and 2003: Access and Activating the Data Analysis Add-in

The data used are in carsdata.xls

• In the Data Group select the Data Analysis Add-in
• Select Regression Analysis
  

We select OK and fill out the dialog box as follows















We obtain





INTERPRETING THE REGRESSION SUMMARY OUTPUT

The key output is given in the Coefficients column in the last set of output:

• b₁ = 0.8 (the Intercept coefficient)
• b₂ = 0.4 (the Coefficient of HH SIZE : the slope coefficient)
  

Thus the fitted line is: y = 0.8 + 0.4 x
or CARS = 0.8 + 0.4 HHSIZE

The regression statistics outyput gives measures of how well the model fits the data. In particular

• R² = 0.8 which measures the fit of the model
  This means that 80% of the variation of y_i around ybar is explained by the regressor x_i
• Standard error = 0.365 which measures the standard deviation of y_i around its fitted value.

The remaining output (ANOVA table and t Stat, p-value, .... ) is used for statistical inference.