Question

A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 Σx = 55 Σy = 55 Σx2 = 385 Σy2 = 385 Σxy = 220 Refer to Exhibit 14-1. The least squares estimate of b0 equals _____

Answer 1

b=11

Explanation:

Given that

n=10, ∑x=55 , ∑y=55 ∑xy=220

`\sum x^2=385,\sum y^2=385`

Lets take linear equation

y= ax + b

By using regression method we know that

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

`b=(\sum y-a\sum x)/(n)`

Now by putting the values

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

`a=(10* 220-55* 55)/(10* 385-(55)^2)`

a= -1

`b=(\sum y-a\sum x)/(n)`

`b=(55+55)/(10)`

b=11