05/11/2022, 14:16
Interpret Regression Coefficient Estimates - {level-level, log-level, level-log & log-log regression} - Curtis Kephart
Teaching - Curtis Kephart‎> E
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Interpret Regression Coefficient Estimates - {level-level, log-level, level-log & log-log regression}
Interpreting Beta: how to interpret your estimate of your regression coefficients (given a
level-level, log-level, level-log, and log-log regression)?
Assumptions before we may interpret our results:
The Gauss–Markov assumptions* hold (in a lot of situations these assumptions may
be relaxed - particularly if you are only interested in an approximation - but for now
assume they strictly hold).
* If you're interested in more details, read the discussion here, or check out your textbook.
Our coefficient estimates (our estimates of
below) are statistically significant and
practically significant.
With a multivariate model, we assume that other independent variable(s) (x_2, x_3,
... x_n) are held constant.
Model
Dependent or Independent
Response
or
Variable
Explanatory
(y)
Variable
(x)
Level-level Regression
y
x
Running a Regression (Using R Statistics Software)
Step-by-step example of how to do a regression using R statistics software
(including the models below). I'll walk through the code for running a
multivariate regression - plus we'll run a number of slightly more
complicated examples to ensure it's all clear.
Video 16:30 - www.youtube.com/watch?v=Ktks5K95uQM
Interpretation of β
Video Review
Given a change in x,
Given reader requests, I created short video explanations of
how much do we expect y to change by?
how to interpret regression estimates
Δy=β1Δx
Interpreting Level-Level Regression Coefficient
Estimate Results
“If you change x by one,
we’d expect y to change by β1"
We run a level-level regression and interpret the regression
coefficient estimate results. Simple example of regression
analysis with a level-level model.
Video 5:00 - www.youtube.com/watch?v=TJACbJspao0
%Δy=100⋅β1⋅Δx
“if we change x by 1 (unit), we’d expect
our y variable to change by
100⋅β1 percent”
Log-Level Regression
x
Log-Level Regression Coefficient Estimate
Interpretation
We run a log-level regression (using R) and interpret the
regression coefficient estimate results. A nice simple example of
regression analysis with a log-level model.
Video 6:40 - www.youtube.com/watch?v=wXC2kViEGz8
Technically, the interpretation is the following:
but the quoted interpretation is approximately true
for values -0.1 < β1 < 0.1 (and it's much easier
to remember.)
Δy=(β1/100)%Δx
Level-Log Regression
y
"If we increase x by one percent,
we expect y to increase by (β1/100) units
of y."
Level-Log Regression Coefficient Estimates
We run a level-log regression and help understand the
regression coefficient estimates. A nice simple example of
regression analysis.
Video 6:50 www.youtube.com/watch?v=L9ZL6_DB4fQ
Note, you cannot include obs. for which x<=0 if x is
then logged. You either can't calculate the regression
coefficients, or may introduce bias.
%Δy=β1%Δx
Log-Log Regression
“if we change x by one percent,
we’d expect y to change by β1 percent”
Note, you cannot include obs. for which x<=0 if x is
logged. You either can't calculate
the regression coefficients, or may introduce bias.
Log-Log Regression Coefficient Estimate Results
We do a log-log regression and explain the regression
coefficient estimate results. Simple example of regression
analysis with a log-log model.
Video 5:30 www.youtube.com/watch?v=NZCSt9Wkpkl
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Curtis K, Jun 12, 2013, 4:47 PM
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