Question

The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.)
x 4 5 2 6 9
y 4 6 2 7 7
The regression equation is y (with a hat) = ______ + _______
When X is 7 this gives y (with a hat) = _________

Answer 1

Answer:

yhat=1.36+0.74x

when x=7 then yhat=6.54

Step-by-step explanation:

Th regression equation is

yhat=a+bx

where slope b is

$b=\frac{nsumxy-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }$

and intercept a is

a=ybar-bxbar

x   4   5   2   6    9

y   4   6   2   7    7

xy 16 30  4  42  63

x² 16 25  4  36  81

n=5.

sumx=26.

sumy=26.

sumx²=162.

sumxy=155.

$b=\frac{5*155-(26)(26)}{5*162-(26)^{2} }$

$b=\frac{99}{134 }$

b=0.7388

b=0.74 (rounded to 2 decimal places)

xbar=sumx/n=26/5=5.2

ybar=sumy/n=26/5=5.2

a=ybar-b*xbar

a=5.2-0.7388*5.2

a=5.2-3.8418

a=1.3582

a=1.36 (rounded to 2 decimal places)

Thus, the required regression equation is

yhat=1.36+0.74x

When x is 7 this gives yhat

yhat=1.36+0.74*7

yhat=1.36+5.18

yhat=6.54