In such situations I have found neural networks to be versatile and can figure out almost any kind relationship between the features and the dependent variable.

You need to do simple regression and find the residuals. According to large or unacceptable values of residuals, you need to eliminate few of the data to lower MSE.

Hola Satanik, te recomiendo que descargues el trial Risk Simulator RS que corre en excel y en uno de los modelos o ejemplos tienes la simulación para determinar el menor valor p que entrega el menor MSE para la correlación

Envio reporte de corrida con el simulador RS

Te recomiendo revises el manual del programa. Encontraras que el software puede realizar la simulación miles de veces para encontrar el el minimo error y el mejor pronostico. Si analizas, el valor U de Thail mas cercano a cero te asegura el mejor modelo para tus pronósticos. Ademas si primero calculas los parámetros p,d,q en AUTO ARIMA, podrás realizar el mejor pronostico.

Revisa el modelo resuelto en excel.

Bien satanik, suerte en tu trabajo academico

Jaime Gutierrez

Satanik -

Experimenting with scatterplots to see how each independent variable relates to the dependent variable, and to each other if you are concerned about collinearity, could be very helpful, though how they might interact in various ways might still be difficult to assess. You may find a good deal of information by researching "model selection," but graphics can be helpful. Once you have some candidate models, you could plot results for two or more at a time using "graphical residual analysis." You could plot predicted y on the x-axis, and estimated residuals on the y-axis and if results for two or more models are on the same scatterplot, make comparisons. To avoid overfitting to the particular sample selected, you might try some kind of "cross-validation." If you could try the graphical residual analysis comparison for different models, using more than one good sample, that could be highly informative. That is, do the comparison with one sample, and then do it again with another. If you have the data, that could be interesting and informative, I think.

Don't forget heteroscedasticity. See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and updates.

Anyway, those are some thoughts on this.

Cheers - Jim

James R Knaub Thank you so much sir, for your time and such an insightful answer. I will follow your suggestion and update. Thanks a million.

Satanik -

You asked about mean square errors. You might consider the estimated variance of the prediction errors. For the estimated residuals alone, we can minimize the sum of weighted squares of estimated residuals, with respect to the regression coefficients, solving for those coefficients. Minimizing the sum of squares of estimated residuals is not ideal when the data itself can show you the regression weight that needs to be used. (See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity for regressions of form y = y* + e.) Ken Brewer warned that a large sample size is needed for accurate estimates leading to these regression weights, but I think that in general, you don't need a large sample size to do better than assuming homoscedasticity, meaning all weights are equal, which many automatically do assume.

To explain:

Please note that heteroscedasticity is expected when predictions are not all the same size. (See above link.) Larger predictions/sizes should be associated with larger sigma for estimated residuals. So when you think of the "mean square error" with regard to estimated residuals, regression coefficients are designed to minimize the sum of squared estimated residuals, but this should be a weighted sum of squares, dependent on size and the coefficient of heteroscedasticity. This weight is the regression weight.

The simplest case showing this development can be found on page 2 here:

https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys

A more involved case is shown on pages 597 and 598 in https://www.researchgate.net/publication/261534907_WEIGHTED_MULTIPLE_REGRESSION_ESTIMATION_FOR_SURVEY_MODEL_SAMPLING

The idea is to minimize "Q," the sum of the squares of the random factors of the estimated residuals, which is the sum of weighted squares of estimated residuals. Q is minimized simultaneously for all regression coefficients, including the intercept term when used.

Here is the regression weight format:

w = z^( -2 gamma)

There is a subscript (i) for the w and the z. Here, z is the size measure. The best one is the best predicted y value, but a preliminary, say OLS value can be used when estimating the coefficient of heteroscedasticity, gamma.

This is important because minimizing the square estimated residual should be constrained by the use of a regression weight, whose natural value is found in several examples in the following:

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

Further information is found in the link I gave in my previous response, including the updates. A tool is given to help decide on a coefficient of heteroscedasticity to then determine the regression weight 'formula.' Your software should use the right regression coefficients if it allows you to enter the regression weights.

Cheers - Jim