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I am trying to run regression on financial data in R. I am new to regression analysis so I am finding it to difficult to interpret certain scenarios. I have the code as follows:

Regression analysis

fit <- lm(fiveMinReturns~RegressionData, data=maindata) summary(fit) # show results

Correlation

cor(maindata$fiveMinReturns,maindata$RegressionData,use="everything")

My output is:

Call: lm(formula = fiveMinReturns ~ RegressionData, data = maindata)

Residuals: Min 1Q Median 3Q Max -0.205790 -0.001144 -0.000062 0.001117 0.156418

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.346e-05 8.785e-06 7.223 5.09e-13 ***

RegressionData 1.597e-07 1.432e-08 11.155 < 2e-16 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.004035 on 210912 degrees of freedom Multiple R-squared: 0.0005896, Adjusted R-squared: 0.0005849 F-statistic: 124.4 on 1 and 210912 DF, p-value: < 2.2e-16

cor(maindata$fiveMinReturns,maindata$RegressionData,use="everything") [1] 0.02428219

p-value is very small that means two variables are tightly coupled, but correlation is small too.

My question is how do I evaluate this situation? Can we say that this equation will give correct results almost every time?Which scenario suggests both p-value and correlation both to be really small? What measures should i take to improve the result?

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1 Answer 1

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A p-value does not mean the values are highly correlated, just that its highly unlikely to have arrived at your results, under your model, assuming they are not related. All you can conclude is that they are not unrelated (i.e., $\rho \neq 0$. The correlation gives an actual magnitude of the correlation, which in your case is small. There is no inconsistency here.

To improve your correlation, you'll need a better model. Also, neither correlation nor p-value speak to the accuracy or precision of your model's output. You'll need cross-validation to determine that.

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