Model
|
Dependent
or Response Variable
(y)
|
Independent
or Explanatory
Variable
(x)
|
Interpretation
of β
Given
a change in x,
how much do we expect y to change by?
|
Video
Review
Given
reader requests, I created short video explanations of how to
interpret regression estimates
|
Level-level Regression
|
y
|
x
|
Δy=β1Δx
“If you change x by one,
we’d expect y
to change by β1"
|
Interpreting Level-Level Regression Coefficient Estimate
Results 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
|
|

|
x
|
%Δy=100⋅β1⋅Δx “if we change x by 1 (unit), we’d expect our y variable to change by 100⋅β1 percent”
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.)
|
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
|
|
y
|

|
Δy=(β1/100)%Δx
"If we increase x by one
percent,
we expect y to increase by (β1/100) units
of y."
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.
|
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
|
Log-Log Regression
|

|

|
%Δy=β1%Δx
“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
|
|
 Updating...
Curtis K, Jun 12, 2013, 4:47 PM
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