To find the equation of the least squares line ÿ = a +bx.
Age Let x be age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For instance, the first data pair says that 5% of all fatal accidents involving 37-year-olds are due to failure to yield the right of way. The Wall Street Journal article referenced in Problem 5 reported the following data:
|
x
|
37
|
47
|
57
|
67
|
77
|
87
|
|
Y
|
5
|
8
|
10
|
16
|
30
|
43
|
(a) Sketch a scatter diagram displaying the data.
(b) Confirm the given sums Σx, Σy, Σx², Σy², Σxy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least squares line ÿ = a +bx.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point (x, y) as one of the points on the line.
Complete parts (a) through (e), given Σx = 372, Σy = 112, Σx² = 24,814, Σy² = 3194, and Σxy = 8254, and r ≈ -0.943.
(f) Predict percentage of all fatal accidents due to failing to yield the right of way for 70-year-olds.