The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a strong linear pattern. With g 1x 2 x2 2 5 1000 and g 1x 2 x2 1 y 2 y2 5 8577, the least-squares line is y^ 5 2936.22 1 8.577x.

a. Because 1 lb 5 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y 5 0.4536(old y).
What is the equation of the least-squares line when y is expressed in kilograms?

b. More generally, suppose that each y value in a data set consisting of n (x, y) pairs is multiplied by a conversion factor c (which changes the units of measurement for y). What effect does this have on the slope b (i.e., how does the new value of b compare to the value before conversion), on the intercept

a, and on the equation of the least-squares line? Verify your conjectures by using the given formulas for b and a.
(Hint: Replace y with cy, and see what happens—
and remember, this conversion will affect y.)

Transcribed Image Text:

x 200.1 210.1 220.1 230.1 240.0 y 813.7 785.3 960.4 1118.0 1076.2