Question

Which equation of the least squares regression line most closely matches the data set?

Note: The variable x represents the years after 1970.

Y= -5.7x-67
Y= -0.98x+65
Y= -0.17x+76
Y= -5.7x +67

Answer 1

D.
`y = -5.7x + 67`

Explanation:

Let us take the year 1970 as the 0th year.

So, the corresponding table of values is,

x y

0 65

2 58

4 45

6 32

8 21

Using the linear regression calculator, we see that,

The closest equation of the regression line is
`y = -5.7x + 67`.

Answer 2

Judging by the first and last points (0, 65), (8, 21), the slope is about -44/8 = -5.5 and the y-intercept is about 65.

The 4th selection is appropriate.