Question 4.155

image 57. Consider again your work on the engine displacement and gas mileage data set in Exercise 44. What if there was a typo, and all of the engine displacements in the data set needed to be adjusted downward by the same amount? Explain how this change would affect the following, and why. Increase, decrease, or no change?

  3. intercept
  4. Slope
  5. Correlation coefficient

4.2.57

(a) Decrease. Since all of the -values are decreased will also decrease. Therefore, will decrease. (b) No change. The -values aren't changed. (c) Increase if , no change if , and decrease if . Since and stay the same and decreases, will increase if , no change if , and decrease if . (d) No change. Since , and all stay the same, stays the same. (e) No change. The correlation coefficient is where and . Since the -values aren t changed, and aren't changed. Since and are decreased by the same amount, and aren't changed. Since the number of data values hasn't changed,hasn't changed. Therefore does not change.