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Least Squares Regression Line (LSRL)
Transcript of Least Squares Regression Line (LSRL)
Equation of a Regression Line
is a straight line that describes how a response variable y changes as an explantory variable x changes. We often use a regression line to predict the value of y for a given value of x.
In simple terms: The regression line shows the relationship between x and y.
b= y intercept
How to do all
of this on your
plug numbers into list 1 and 2
2nd stat plot
1: turn plots on (plot 1) and
use list 1 and 2
stat --> calc
#8: LinReg(a+bx), choosing
list 1 and list 2, and storing
enter, then graph
It's a line that best fits the data.
Only works for linear data
If doing by hand, different people would draw the line in different places at different slopes, etc.
Therefore we want the line as close to the points in the vertical direction.
Basically . . . . .
But statistically, we call it y = a + bx
a = y - bx
b = r
EVERY regression line goes through (x, y).
The slope identifies how much of a change there is in y when x increase by 1.
As correlation weakens, y moves less in response to changes in x.
Allows us to predict a value using the relationship.
The regression line is created by finding the differences between the "line" and the observed values. The "line" that makes the best fit becomes the regression line.
We want those vertical distances to be as small as possible.
The small the distances, the smaller our error in predicting y.
Once you have your LSRL,
you can plug in the x value
you want to predict a y
value for and simplify.