Question 6.86

51. Consider the dataset below:

4 8
7 12
  1. Calculate .
  2. Calculate the correlation . Round your answer to two decimal places. (Why should you not be surprised at this result?)
  3. Use your results from parts (a) and (b) to find the slope and -intercept of the least-squares regression line.
  4. In this case, did you really need to work through the procedure for finding the least-squares regression line in order to find the equation of the best-fitting line? Explain.

51.

(a)

(b)

(c)

(d) No. You can find the equation using basic algebra. Using the slope formula, we get . The equation of the line will have the form . Substitute one of the two points into this equation and solve for , which gives . The equation is .