Find the equation for the least squares regression line of the data described below.

Question

Bruce keeps detailed information about his model airplane collection. The data includes not only the characteristics of each model, but also the time it took to assemble it. He is thinking of buying a new model airplane and decided to look at this information to understand how long assembly might take.
From his data, Bruce found the number of pieces in each model, x, and how many minutes each took to assemble, y.
Pieces - Assembly time
45 - 30
46 - 33
67 - 37
70 - 39
90 - 52

Answer 1

To find the equation for the least squares regression line, we first need to calculate the values of x^2, y^2, and xy for the data given:

x y x^2 y^2 xy
45 30 2025 900 1350
46 33 2116 1089 1518
67 37 4489 1369 2483
70 39 4900 1521 2730
90 52 8100 2704 4680

Next, we calculate the sums of x, y, x^2, y^2, and xy:

Σx = 318
Σy = 191
Σx^2 = 21630
Σy^2 = 7583
Σxy = 12361

Now we can use these values to find the equation for the least squares regression line:

m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
m = (5(12361) - (318)(191)) / (5(21630) - (318)^2)
m = (61805 - 60638) / (108150 - 101124)
m = 1167 / 7026
m = 0.166

b = (Σy - mΣx) / n
b = (191 - (0.166)(318)) / 5
b = 191 - 52.788
b = 138.212

Therefore, the equation for the least squares regression line is:
y = 0.166x + 138.212