Showing Page:
1/1
Whenever we ask a computer to perform simple linear regression, it uses these equations
to find the best fit line, then shows us the parameter estimates. Sometimes the symbols β
ˆ
0
and β
ˆ
1
are used instead of b
0
and b
1
. Even though these symbols have Greek letters in them,
the “hat” over the beta tells us that we are dealing with statistics, not parameters.
Here are the derivations of the coefficient estimates. SSR indicates sum
of squared residuals, the quantity to minimize.
SSR
=
n
X
i
(
y
i
(
β
0
+
β
1
x
i
))
2
(9.1)
=
n
X
i
y
2
i
2
y
i
(
β
0
+
β
1
x
i
)+
β
2
0
+2
β
0
β
1
x
i
+
β
2
1
x
2
i
(9.2)

Unformatted Attachment Preview

Whenever we ask a computer to perform simple linear regression, it uses these equations to find the best fit line, then shows us the parameter estimates. Sometimes the symbols βˆ0 and βˆ1 are used instead of b0 and b1. Even though these symbols have Greek letters in them, the “hat” over the beta tells us that we are dealing with statistics, not parameters. Here are the derivations of the coefficient estimates. SSR indicates sum of squared residuals, the quantity to minimize. n SSR = X i =1 n = X i =1 (yi − (β0 + β1x i ))2 yi2 − 2yi (β0 + β1x i )+ β02 +2 β0β1x i + β12x 2i (9.1) (9.2) Name: Description: ...
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.
Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4