by Russell A. Poldrack
Posts mit dem Label R werden angezeigt. Alle Posts anzeigen
Posts mit dem Label R werden angezeigt. Alle Posts anzeigen
Samstag, 11. Mai 2019
Statistical Thinking for the 21st Century
Found an interesting Open Source online book about statistics and R:
Statistical Thinking for the 21st Century,
by Russell A. Poldrack
by Russell A. Poldrack
Sonntag, 9. August 2015
Understanding Multiple Regression with Dummy Variables
Recently, I played a bit with a special case of linear regression.
My real-world problem was that I had measured WLAN reception at different distances with 2 devices - a smartphone and a tablet computer. Now, there is a linear relationship between the distance and the log of the received power of the signal. But since the tablet has better antennae than the smartphone the values are shifted by a certain amount. If only I could do something like a combined linear regression over both sets of data which would give me 2 parallel regression lines with the same slope but different intercepts...
My stats courses were a long time ago and I think we only ever covered simple linear regression anyway. So I searched for "multiple regression" - and found how to do regression when the dependent variable depends on more than one independent variable, iow. when you have a y = f(x1, x2, ...,xn). But I had y1 = f(x) in combination with y2 = f(x)... While I decided to review the definition of simple linear regression to derive something myself I got a tip to take a look at multiple linear regression with dummy variables. Multiple regression with dummy variables is what I wanted - but because the explanations I found when googling around all ended with "and now you just put all that stuff into your stats program" it was not clear how it really works. So, while I did reinvent the wheel it helped me a lot in understanding the matter and I've decided to share my findings. It's actually not complicated at all, so enjoy!
Read more (download PDF) containing a derivation of how it works, showing how that connects to the explanations given in most stats books and tutorials and how to do multiple regression with dummy variables in R (including how to produce the graph shown above).
My real-world problem was that I had measured WLAN reception at different distances with 2 devices - a smartphone and a tablet computer. Now, there is a linear relationship between the distance and the log of the received power of the signal. But since the tablet has better antennae than the smartphone the values are shifted by a certain amount. If only I could do something like a combined linear regression over both sets of data which would give me 2 parallel regression lines with the same slope but different intercepts...
 |
| Finding a combined slope and different intercepts for two sets of data == multiple regression with dummy variables |
My stats courses were a long time ago and I think we only ever covered simple linear regression anyway. So I searched for "multiple regression" - and found how to do regression when the dependent variable depends on more than one independent variable, iow. when you have a y = f(x1, x2, ...,xn). But I had y1 = f(x) in combination with y2 = f(x)... While I decided to review the definition of simple linear regression to derive something myself I got a tip to take a look at multiple linear regression with dummy variables. Multiple regression with dummy variables is what I wanted - but because the explanations I found when googling around all ended with "and now you just put all that stuff into your stats program" it was not clear how it really works. So, while I did reinvent the wheel it helped me a lot in understanding the matter and I've decided to share my findings. It's actually not complicated at all, so enjoy!
Read more (download PDF) containing a derivation of how it works, showing how that connects to the explanations given in most stats books and tutorials and how to do multiple regression with dummy variables in R (including how to produce the graph shown above).
Abonnieren
Posts (Atom)