Auto correlation between dependent and independent variable is always give a better results. However u asking about the VIF. U have to check the VIF should not be negative and also check the predicted R-Square for regression analysis.

Note: Kindly use the quadratic or cubic or special quadratic model for analysis. Done care about the Auto correlation

Refer about the VIF advantages in OLS model.

Thanks for the reply. The dependent variable in question is continuous and therefore, we areplanning to do a linear regression. We have checked VIF and tolerance and found there was little or no multicollinearity. 

Now, when we checked for autocorrelation the value of Durbin-Watson's d was found to be around three. 

Therefore, I would like to know that is this value acceptable?

You speak of autocorrelation for the predictors. Since there is no real assumption on the predictors distribution, I do not see why this would be a problem.

If you have correlation between the predictors, however, it's another debate. But you say you don't have.

If you have autocorrelation of the residuals, that's still another debate. The answer depends on the potential origin of this autocorrelation. For instance, if you have somehow sorted your values between regression, autocorrelation does not really mean anything...

Thanks for the reply. We checked for auto correlation in the residuals. and the Durbin Watson's d is still very around three. What do you suggest?

Have you checked this page?

https://en.wikipedia.org/wiki/Durbin–Watson_statistic

Well, try to understand its origin. Or try to model it using general least squares (but may be difficult to build a model without understanding where the correlation comes from). Or check using bootstrap/permutations/simulations/any other approach how far it invalidates your results.

As evoqued above, check first if the order of the data is really "random" (that is, the same than the order of data collection for a randomized experiment) or was somehow sorted for any reason... including a lack of randomization in the data collection process.

Quite impossible to say more without any hint about the experiment context.

Thanks for the reply. I will try to do as you said and let you know the results...

Based on study correlation interpretation will differ. IF d=3 means it indicates negative correlation

http://www.businessdictionary.com/definition/Durbin-Watson-Statistic.html

R  you  talking  about  cross section  or  time  series  data.

If  your  data  is  time  series  then  Durbin Watson  of 3  is  far  from  2  but  we cannot tell if  3 is  significant untel we compare it with the  Durbin Watson  table  critical value.  Furthermore  I  recommend  testing  if  your variables  are stationary and  cointegrated.

If  your  data is cross sectional  then run  residual  analysis  to eliminate  outliers from  your  data  if  they  exist  in  your data

I think what is missing is an understanding of what may be driving the autocorrelation. Does your data have a nested structure (e.g., individuals nested within classrooms or data points nested within individuals over time)? Or as I think was mentioned above is it a time-series regression? 

The answer to either will influence the approach you take to resolve the problem. For instance, if you have a nested data structure you may need to consider a multilevel modeling approach. If you are dealing with time series data, entering a time-lagged predictor may resolve your autocorrelation problems. 

I can't say for sure if the properties of your data are in line with either of the descriptions above, but hopefully that can help inform your thinking about the approaches available to you. 

You can check these links for details and guidelines about regression analysis and testing for autocorrelation:

https://en.wikipedia.org/wiki/Regression_analysis

https://books.google.fr/books?id=SdaGAwAAQBAJ&pg=PA379&redir_esc=y#v=onepage&q&f=false

http://stat.smmu.edu.cn/DOWNLOAD/ebook/econometric.pdf

In addition, it may be of practical interest to do an independent component analysis (ICA) in order to extract some independent predictors, if such predictors exist.

Hi

In order to develop the tests of autocorrelation and interpret the results, the following points need to be studied.

1. Autocorrelation is a characteristic of data in which the correlation between the values of the same variables is based on related objects. It violates the assumption of instance independence, which underlies most of the conventional models. It generally exists in those types of data-sets in which the data, instead of being randomly selected, is from the same source.

2. The most common form of autocorrelation is first-order serial correlation, which can either be positive or negative.

- Positive serial correlation is where a positive error in one period carries over into a positive error for the following period.

- Negative serial correlation is where a negative error in one period carries over into a negative error for the following period.

3. There is a very popular test called the Durbin Watson test that detects the presence of autocorrelation. If the researcher detects autocorrelation in the data, then the first thing the researcher should do is to try to find whether or not it is pure. If it is pure, then one can transform it into the original model that is free from pure autocorrelation.

4. You can test for autocorrelation with:

i. A plot of residuals. Plot et against t and look for clusters of successive residuals on one side of the zero line. You can also try adding a Lowess line, as in the image below.

ii. A Lagrange Multiplier Test.

iii. A correlogram. A pattern in the results is an indication for autocorrelation. Any values above zero should be looked at with suspicion.

iv. The Moran’s I statistic, which is similar to a correlation coefficient.

5. The test can be developed using different Statistical packages. Examples are:

Technology Options

i. In Minitab:

Click Stat > Regression > Regression > Fit Regression Model. Click “Results,” and check the Durbin-Watson statistic.

ii. SAS: Find directions here on the UCLA website.

iii. MATLAB: The procedure can be found here on the Mathworks site.

iv. SPSS: From the main regression dialog box, click Statistics. Check the box for Durbin-Watson (in the Residuals section of Linear Regression Statistics).

Regards,

Zuhair