1
$\begingroup$

I have done a regression model where i determine the number of cubes (independent variable) based on the amount of units i started with for each product type (dependent variables, X1, X2, X3, X4, X6, X9, X10, X15). But i would like a second opinion on the results, because the tests for heteroscedasticity i did (Breusch-Pagan and white test) suggests my data has heteroscedasticity. But i think it is because i have alot of data (500 000 observations). Looking at the graphs below i don't seem to pick up much heteroscedasticity, although there do seem to be outliers in my data. But i would like to have a second opinion and want to know does my results look fine so that i can use this regression model and can assume (1) my residuals close enough to a normal distribution and (2) there is little sign of heteroscedasticity?

Here is the coefficients

Coef Estimate Std. Error t value Pr(>|t|) X1 0.023493012 0.000497393 47.23233675 0 X2 0.002248871 0.000777214 2.893502743 0.003811022 X3 0.069934116 0.000484908 144.2215372 0 X4 0.084532734 0.000883563 95.67252408 0 X6 0.014607296 0.000458375 31.86759025 4.43E-221 X9 0.409846348 0.001738917 235.6905778 0 X10 0.128915999 0.000468583 275.1187379 0 X15 0.042864773 0.001276817 33.57157987 6.58E-245

R-squared: 0.8158 Adj R-squared: 0.8158 F-stat: 3.47e+04, p-value < 2.2e-16

Here is all the graphs.

enter image description here

enter image description here

enter image description here

enter image description here

$\endgroup$
  • $\begingroup$ There's very clear indication of heteroskedasticity. There's also suggestion of lack of fit. $\endgroup$ – Glen_b -Reinstate Monica Jul 27 '14 at 1:45
0
$\begingroup$

I don't think you have a heteroskedasticity problem (which is not such a problem anyway, because it only affects the variance of OLS estimates and not their consistency), and your residuals look pretty gaussian to me.

However, I would be worried about endogeneity (or some other form of mis-specification) because of your two last plots: the residuals seem higher for high values of your independent variable (especially when the indepent variable is above 1) which means your model "undershoots" for the high values and "overshoots" for low values of the independent.

$\endgroup$
  • 1
    $\begingroup$ You can't readily assess normality in the presence of heteroskedasticity, since the hetero makes the residuals a mixture of errors with different distributions. As for whether hetero matters much depends on what he's using it for, and in exactly what manner. If he wants confidence intervals around predicted means, for example, he has a serious problem. $\endgroup$ – Glen_b -Reinstate Monica Jul 27 '14 at 1:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.