I have the following multiple linear regression model:
Call:
lm(formula = Y ~ X1 + X2 + X2 + X3 + X4 + X5 + X6 + X7,
data = my.model, na.action = na.omit)
Residuals:
Min 1Q Median 3Q Max
-43.836 -1.507 0.010 1.485 46.231
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.0244927 0.0245157 -0.999 0.318
X1 -0.3484619 0.0134383 -25.931 <2e-16 ***
X2 0.1195273 0.0106940 11.177 <2e-16 ***
X3 0.1224587 0.0108849 11.250 <2e-16 ***
X4 -0.0010173 0.0028247 -0.360 0.719
X5 0.5496942 0.0156319 35.165 <2e-16 ***
X6 -0.2287941 0.0145018 -15.777 <2e-16 ***
X7 -0.2315801 0.0146361 -15.823 <2e-16 ***
X8 0.0005465 0.0003595 1.520 0.128
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.936 on 35849 degrees of freedom
(12534 observations deleted due to missingness)
Multiple R-squared: 0.05968, Adjusted R-squared: 0.05947
F-statistic: 284.4 on 8 and 35849 DF, p-value: < 2.2e-16
The model is affected by multicollinearity but my question is about the forecast, so this shouldn't be an issue.
I checked the absolute values of my model forecast and compared against the actual Y absolute values. The average of the absolute predicted values is significantly lower than the absolute observed values mean:
> lm1.predict = predict(lm1, mydata)
> mean(abs(lm1.predict))
[1] 0.3294776
> mean(abs(mydata$Y))
[1] 1.206954
Does this mean that the linear regression variables I am using tend to underestimate the outcomes? Can any other conclusion be derived from this simple comparison?