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The simple linear regression model
1.1
The linear deterministic model
A simple deterministic relationship between two variables (here
x
and
y
) is a linear relation-
ship
y
=
β
0
+
β
1
x
You remember from algebra and geometry that this is the equation of line with a slope
β
1
and a y-intercept
β
0
. What is the value of
y
when
x
= 0? How much does the value of
y
change for each unit change
x
.
Remember all of my comments on populations and parameters? If, say, we all were God (a
belief not in contrast with some religions!
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), we would know exactly the values of y (because
we knew exactly the values of
β
0
,β
1
) for each given value of x.
Conventionally, we call
x
the
independent variable
and
y
the
dependent variable
.
For example, let
y
≡
the selling price for a house and
x
≡
the size of the house - in square
feet (are you getting a feel for how we assign
x
and
y
?).
And you know that the value of
y
when
x
= 0 is 25
,
000. And you know that the change in
y
for each square foot increase is 75.
Then you know
β
0
= 25000 and
β
1
= 75 and you can write
y
= 25000 + 75
x
as the deterministic relationship between size of house and its selling price
Here is a remark: A
scatterplot
of house and selling price if this relationship is true should
look like?
In
R
housesize<-c(1000,1000,1500,1500,1700,1250,2000,2150,2150)
#the house sizes in square feet
sellingprice<-c(25000000,27000000,38000000,37299999,
42500000,31350003,50000000,53800000,53700000)
#the selling prices in dollars
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This is meant to be funny
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