Run regression

You should have detected a positive relationship between education and income. We are interested in how such a relationship is significant -- that is, the explanatory power of Education on Income. To see this, we need to apply an econometric model. We will run linear regression now. The model is the following:

Income_i = $$\beta_{0}^{}$$ + $$\beta_{1}^{}$$Sex_i + $$\beta_{2}^{}$$Education_i + $$\epsilon_{i}^{}$$.

$\beta_{0}^{}$ is the intercept, $\beta_{1}^{}$ is an intercept dummy, and $\beta_{2}^{}$ is the slope coefficient. Here, we don't make any assumption on the statistical distribution on $\epsilon_{i}^{}$. That is unnecessary for an ordinary least squares (OLS) regression. For more detail on OLS, see Statistics Refresher.

Back to Excel now. Select the data range, including the data labels. Select Data Analysis... option from Tools menu. Select Regression option and click .

You will see the Regression dialogue box. Now you need to do the following:

• Input Y Range: $\Rightarrow$ Click on to change to the selection view. Left-click on cell A1, hold the left mouse button and drag the cursor down to cell A26. This will select the range A1:A26.¹ Click on to return to the normal view.
• Input Y Range: $\Rightarrow$ Do the same as above. Select the range B1:C26 as explanatory variables.
• Tick the Labels box.
• Output options Check New Worksheet Ply:

  $\Rightarrow$

  Tick Residuals if you will.

  $\Rightarrow$

  Tick Residual Plots if you will.

  $\Rightarrow$

  Tick Line Fit Plots (I find this one more useful).

• Click

This will produce the following output:

You have also obtained the following scatter plot, thanks to the Line Fit Plot option.

For the interpretation of this output, refer to Statistics Refresher.

¹ The expression A1 means in Excel that cell A1 is absolutely referenced. For more detail, consult Excel help on Absolute Reference.

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