Question

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

note: the variable x represents the years after 1972.

x y
1972 -28
1974 8
1976 39
1978 62
1980 98

a. y = 0.06x - 28
b. y = 15.3x - 25.4
c. y = 15.3x + 25.4
d. y = 1.03x - 56

Answer 1

B. y^ = 15.3x - 25.4

Answer 2

b. y = 15.3 x - 25.4

Explanation:

Here, x represents the number of years after 1972,

Thus, the table of variables will be,

x 0 2 4 6 8

y -28 8 39 62 98

By the above table,

We have,

`\sum x = 20`

`\sum y = 179`

`\sum x^2=120`

`\sum xy = 1328`

Since, the linear regression equation is,

y = b + ax

Where,

`b=(n(\sum xy)-(\sum x)(\sum y))/(n(\sum x^2)-(\sum x)^2)`

`a=((\sum y) (\sum x^2)-(\sum x)(\sum xy))/(n(\sum x^2)-(\sum x)^2)`

By substituting the values,

We get, b = -25.4 and a = 15.3

Thus, the required linear regression equation is,

y = 15.3 x - 25.4

⇒ Option b is correct.