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 _____

Respuesta :

Answer:

b=11

Step-by-step explanation:

Given that

n=10,  ∑x=55  , ∑y=55   ∑xy=220

[tex]\sum x^2=385,\sum y^2=385[/tex]

Lets take linear equation

y= ax + b

By using regression method we know that

[tex]a=\frac{n\sum xy-\sum x \sum y}{n\sum x^2-(\sum x)^2}[/tex]

[tex]b=\frac{\sum y-a\sum x}{n}[/tex]

Now by putting the values

[tex]a=\frac{n\sum xy-\sum x \sum y}{n\sum x^2-(\sum x)^2}[/tex]

[tex]a=\frac{10\times 220-55\times 55}{10\times 385-(55)^2}[/tex]

a= -1

[tex]b=\frac{\sum y-a\sum x}{n}[/tex]

[tex]b=\frac{55+55}{10}[/tex]

b=11