Compare the sum of squared residuals for the lines in Examples 1 and 3.

Approach Use a table to compute ∑residuals² using the predicted values of y, ŷ, for the equations in Examples 1 and 3.

Data from Example 1

The data in Table 5 represent the club-head speed and the distance a golf ball travels for eight swings of the club. We found that these data are linearly related .

Data from Example 3

Use the golf data in Table 5.

Find the least-squares regression line.

Draw the least-squares regression line on the scatter diagram of the data.

Predict the distance a golf ball will travel when hit with a club-head speed of 103 miles per hour (mph).

Determine the residual for the predicted value found in part (c). Is the distance in Table 5 above average or below average among all balls hit with a swing speed of 103 mph?

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Table 5 Club-head Speed (mph) x Distance (yd) y (x, y) 100 257 (100,257) 102 264 (102,264) 103 274 (103,274) 101 266 (101,266) 105 277 (105,277) 100 263 (100,263) 99 258 (99,258) 105 275 (105,275)