Question 2.50

2.50 Residual for Texas

Refer to Example 2.16 (page 89). Texas spent $90.5 million on education and has a population of 26.8 million people.

  1. Find the predicted education spending for Texas.
  2. Find the residual for Texas.
  3. Which state, California or Texas, has a greater deviation from the regression line?

There is a residual for each data point. Finding the residuals with a calculator is a bit unpleasant, because you must first find the predicted response for every x. Statistical software gives you the residuals all at once.

Because the residuals show how far the data fall from our regression line, examining the residuals helps us assess how well the line describes the data. Although residuals can be calculated from any model fitted to data, the residuals from the least-squares line have a special property: the mean of the least-squares residuals is always zero.