# Interpretation of linear regression

Call:
lm(formula = log.ret ~ vol.252)

Residuals:
Min        1Q    Median        3Q       Max
-0.229112 -0.004682  0.000231  0.005009  0.153705

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.0003142  0.0001597   1.967   0.0492 *
vol.252     -0.0006912  0.0008623  -0.802   0.4228
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01148 on 23314 degrees of freedom
(251 observations deleted due to missingness)
Multiple R-squared:  2.756e-05, Adjusted R-squared:  -1.533e-05
F-statistic: 0.6425 on 1 and 23314 DF,  p-value: 0.4228


This is plotting a linear regression using the log prices of the S&P500 and the 252 day close volatility.

I am using the TTR package to work out the 252 close volatility and also the log prices.

The best fit is close to zero. What exactly is this saying? Is this showing mean reverting nature?

I am actually trying to recreate this example: http://epchan.blogspot.com/2016/04/mean-reversion-momentum-and-volatility.html

• There does not seem to be much relation between EP Chan's article which considers volatility as a function of the time interval (from 1 minute to 17 hours) and yours which is based on daily volatility. He varies the time interval, you have it constant (1 day), if I understood correctly. What are you trying to do? – Alex C Jul 10 '17 at 3:03
• Ok - Well I was trying to see if I could replicate his study. I wanted to see for myself the mean reverting nature of the S&P500 on a interday basis. So that means, he must have prepped the data on his 1-10 hour range for over the sample period? Ernie is using sample period: 20130116-20160115 for SPY. No other way to fit all of it on one graph. I guess the log variance he is plotting is per minute basis on his X axis? I am not sure on the methodology used to re-create what Ernie did. I think its a good skill to know because I wanted to learn how to assess conditions of different products – Andrew Bannerman Jul 10 '17 at 16:40