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")  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?