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Module 9: Correlation & Simple Regression (Drawing a line through the…
Module 9: Correlation & Simple Regression
Drawing a line through the data (linear regression)
Simple Linear Regression
X is the "predictor" variable
Y is the "response" variable
How much variability in a response variable is "attributable" to the predictor variable?
R squared = the correlation coefficient squared
Straight line and 1 predictor variable
Y=MX + b
How much does "Y" change when "X" changes?
Slope is "rise over run"
Line of Best Fit "LOBF"
Minimizes the SSE (Sum of Squares Error)
Yi=Bo +b1Xi
"Bo" is intercept
"B1" is the slope
"Slope" tends to be the most important
The "change" in Y for 1 unit change in X
Residual - "How wrong are we?"
SSE = Sum of Squared Errors
How "spread out" the data is from the line.
Wrong Assumptions
We are not assuming "X" causes "Y"
Inference with Regression
Why? To estimate how much the response variable "changes" when the predictor variable "changes"
Sampling Distribution of LOBF?
Y
is the location on Y axis,
b
is the intercept,
X
is the location on the X axis, and
M
is the slope