Question

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

Answer 1

Answer:

b. y = 15.3 x - 25.4

Step-by-step 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,

$b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$

$a=\frac{(\sum y) (\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}$

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.

Answer 2

B. y^ = 15.3x - 25.4