Hi,

First, check up on the assumptions of normality of each of the variables. A scatter plot between the two variables shows you the relationship as linear or not with the best fit line and confidence intervals.

Loglinear conversion is also possible and nonlinear regression

Sure just get it right.. best wishes, David Booth

Hi Bhogaraju

Thanks for your response. So all my DV's are normal and my IV's are not normal. However, I noticed that there is some linearity because the beta is not 0

Normality in the regressors (IV's) is rarely a problem. OLS regression in itself does not require normality of either the IV's or the DV. But it does expect the relationship to be linear. Normality of regressors may (but may not) affect the normality of the coefficient estimates in your regression equation. If coefficients are not normal then standard errors and p-values will be unreliable. This can also happen with normally-distributed IV's. OLS regression produces estimates that are BLUE (Best Linear Unbiased Estimates).

So overcoming the nonlinear relationship should be your focus, not the shape of the IV's.

Be careful how you define your non-linear regression. If you are using rating scales from a survey then your data are technically ordinal, not ratio, scaled. So, do not use exponents or logs (e.g. squares or square roots) to "linearise" your data. These are excellent methods but only when the variables used have real and meaningful zeros (e.g. money, time spent, counts, etc.)

Use bootstrapping to find a useful range of values for your coefficients.

Lebogang Tau -

You stated that "...my IV does not have a linear relationship with any of my DV." But note that "linearity" does not necessarily mean a straight line. You could have polynomial linear regression. However, as David indicated, it is better to correct yourself if needed.

There are other kinds of regression. Perhaps you are really doing counts. But if you have continuous data and a relationship where Yi = yi* + e, where yi* is the predicted y in the ith case, then you generally have weighted least squares (WLS) regression. If the weights are all the same, although they shouldn't be, then you have OLS regression. (Even more generally, usually for time series, not the finite population statistics I think you mean here, you could have autocorrelation and need GLS, generalized least squares regression. You might also have spatial autocorrelation to consider.)

The following resources may be helpful for considering heteroscedasticity, which is a feature, not a bug, including an Excel tool for finding a good value for the coefficient of heteroscedasticity, used in regression weights. In the Excel spreadsheet there is a page noting that default values for the coefficient of heteroscedasticity are possible when your sample size is not large enough to obtain a good estimate. In the formulation I give, Ken Brewer showed why it should be from 0.5 to 1. I've noted that if your smaller cases are less reliable, this tends to bring the best effective value of the coefficient of heteroscedasticity down to 0.5, where Ken suggested 0.75 or 1, but it depends on the application. In an article I list below from the Pakistan Journal of Statistics, I note that more complex models may have effective coefficients of heteroscedasticity closer to zero because they cannot do such a good job of creating the predicted-y values.

Best wishes - Jim.

........

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, with bounds on the coefficient of heteroscedasticity as explained by Ken Brewer,

https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR,

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

with

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

and

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates and references there.

........

PS -

Could you be thinking of multivariate regression, as opposed to multiple regression (though you can have multivariate multiple regression)? You may want to look onto that. - Cheers.

use transformation

In my last link above, https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, there is an update on why you should not use a transformation to handle heteroscedasticity. Also above I noted that "... if you have continuous data and a relationship where Yi = yi* + e, where yi* is the predicted y in the ith case, then you generally have weighted least squares (WLS) regression." I then gave links to information to handle this.

use transformation method!

To determine appropriate regression weights, the links of interest above are repeated here:

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

with

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Note that a sheet in the spreadsheet indicates that when your sample size is too small to obtain an accurate estimate of the coefficient of heteroscedasticity, that a default may be used, depending on application, as noted in a book referenced, written by Ken Brewer. It ideally should be from 0.5 to 1.0. I have found that for a skewed establishment survey, that data quality issues for the smaller respondents may drive the number down to 0.5 or worse when 0.8 might be the more ideal case.

Transformations may not address the heteroscedasticity fully and leave you still having heteroscedasticity, or alternatively you might actually over-compensate. Regardless, you will have results that are no longer as straightforwardly interpretable because you no longer have your original variables. Essential heteroscedasticity is not a bug, but an expected feature. (Two references found under the project I noted above are "Essential Heteroscedasticity," and "Nonessential Heteroscedasticity," which may help you to understand heteroscedasticity better.) Understanding the nature of heteroscedasticity is important.

To use linear regression, your DV must be continuous, then check the assumption of linearity and normality. If the assumption is violated, transform your data.

Transformation of data here is generally not desirable. A quadratic linear or nonlinear regression can be fit by software using a least squares fit, or better, weighted least squares, for any particular sample. (Consider a "graphical residual analysis," and "cross-validation.")

Near normality of residuals is preferable. Data can be distributed in any manner. I worked a great deal with establishment surveys, where data are skewed or highly skewed.

Note -

"Nature and magnitude of heteroscedasticity of estimated residuals in regressions of approximate form

y = y* + (e_0)(z^~gamma),

for finite populations":     

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as determined by Ken Brewer,

and

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

with 

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Have you tried converting the regression model from nonlinear to linear?

most regressions are based on fit the output vs a function dependant to your input. you can use nonlinear regression by the cost of studying the transformed data. for example instead of study growth vs income your new variable should be income at square, or logaritm of income. thats the exception you need to specify.