# Interpreting regression results

I ran the following regression using R.

libor <- ts(diff(Libor))
ois <- ts(diff(OIS))
x <- ts(diff(Repo-OIS))
vix <- ts(diff(VIX))
cds <- ts(diff(CDS))
treasury <- ts(diff(log(P_treasury)))
mbs <- ts(diff(log(P_MBS)))
rrp <- ts(diff(log(RRP)))
axx <- ts.intersect(mbs, treasury, rrp, cds, libor, ois, x, vix)
reg3 <- lm(libor~ois+x+vix+cds+treasury+mbs+rrp, data=axx, subset=418:521)


which gave me the following output:

t test of coefficients:

Estimate  Std. Error t value Pr(>|t|)
(Intercept)  8.6279e-04  8.0537e-04  1.0713  0.28675
ois          1.1427e-01  5.5089e-02  2.0742  0.04076 *
x           -1.0914e-02  2.0758e-02 -0.5258  0.60028
vix         -1.3155e-04  1.8298e-04 -0.7190  0.47394
cds          7.9692e-05  1.0590e-04  0.7525  0.45358
treasury    -3.3914e-01  1.9171e-01 -1.7690  0.08010 .
mbs         -4.0022e-03  1.3883e-02 -0.2883  0.77376
rrp          1.6299e-05  1.5772e-04  0.1033  0.91791


While the variables libor, ois, x ,vix are in percent the variables treasury, mbs and rrp are in log and in million of USD. So it is a lin- log model. The variable treasury increased during the analysed time period by 47% (from 1671382 mio USD to 2461389 mio USD.). Now I want to calculate the impact of the variable treasury on my dependent variable (libor). following my book this is done: Δy=(β1/100)%Δx --> = (-0.33914/100)*47=0.1593958. So I can say, that if the variable treasury is increased by 47% my dependent variable will decline by 0.1593958% or 15.94 basispoints. Is this interpretation correct?

My question arises because in a working paper they calculated (B1*100*47). I couldn't figure out why they multiply their B1 with 100 instead of divide it by 100. Any ideas? Many thanks!

• If libor is a percent value, you shouldn't use ordinary least squares regression. You should use a GLM. Commented Apr 21, 2015 at 10:01

## 1 Answer

Ok. I found the soultion. Since the first difference of a variable in Log- form is approximately the change in percent, you need to multiply your coefficient (B1) with 100 in order to get the impact of the independent variable on the dependent variable in basis points!