(a) Find the least squares regression line. y = (b) Calculate S, the sum of the squared errors. Use the regression capabilities of a graphing utility to verify your results.

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.39+0.1621 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?

A least squares regression line was calculated to relate the length​ (cm) of newborn boys to their weight in kg. The line is weight=−5.59+0.1826 length. A newborn was 48 cm long and weighed 3 kg. According to the regression​ model, what was his​ residual? What does that say about​ him?