1. How Is a Regression Equation Affected by Change in Scale? Large numbers, such as those in the accompanying table, often cause computational problems. First use the given data to find the equation of the regression line, then find the equation of the regression line after each x-value has been divided by 1000. How are the results affected by the change in x? How would the results be affected if each y-value were divided by 1000?
|
x
|
924,736
|
832,985
|
825,664
|
793,427
|
857,366
|
|
y
|
142
|
111
|
109
|
95
|
119
|
2. Testing Least-Squares Property According to the least-squares property, the regres- sion line minimizes the sum of the squares of the residuals. We noted that with the paired data in the margin, the regression equation is yˆ 5 5 1 4x and the sum of the squares of the residuals is 364. Show that the equation yˆ 5 8 1 3x results in a sum of squares of residuals that is greater than 364.