Welcome to clinical data management program using SAS. In this video we'll be discussing about the further concepts of linear regression like in vi we have discussed that vi ever variance inflation factor is used to detect multicollinearity when the independent variables are very much interrelated to each other, then the multicollinearity is more among those independent variables and as a result of the multicollinearity the variance of the independent variables gets inflated and that results in variance inflation factor. So, variance of the estimator regression coefficients is unbounded multicollinearity is said to be a problem with the various addition factors of one or more characters becomes large. So, mostly the researchers they they keep the the keeper benchmark. So, they give say that we if if it is either five or 10 then the political narrative is normal. Any VA fellow any variable having the a pharaoh which is about five or 10 that means the multipolarity is high Those independent variables the VI F is closely related to a statistical call to a statistic called the tolerance where my vi F is basically we know that VA is Vi is equal to one by one minus r square and tolerance is one by VA.

So, that is one minus r square. What are the remedies are VA when vi F is regarded as being too high for variables, the solutions are as follows obtains more data so as to reduce the standard error, obtain better data where the parameters are less correlated record the predictors in a way that reduces correlations. Next, let's come to the concept of the concept of autocorrelation. What do you mean by autocorrelation autocorrelation is when my error terms are correlated with respect to time, that is error term at the time period is correlated to error term the T minus one a time period and a leftover t minus one t minus one a time period is correlated to error terms of t minus two a time period that is the ETS coordinator to et minus valid event as well as correlate to et minus two So, autocorrelation is a mathematical representation of the degree of similarity between a given time series and the last version of itself over successive time intervals, it is the same as calculating the correlation between two different time series, except that the same time series is used twice once in its original form and once lagged one or more time periods autocorrelation is calculated to detect patterns in the data according to the assumption of classical linear regression model, the editor should not be correlated with respect to time, there should not be any autocorrelation with respect to the error terms.

Next come to the concept of the Durbin Watson test devinwatson test is use check for autocorrelation there may h notice there is no correlation an h1 is auto correlation exists. So my dw statistic or D is equal to summation of Ei minus e A minus one whole square divided by summation a square or B is equal to two into one minus rho. So, D stands for the Durbin Watson statistic formula there is two Formula One formula is Equals system submission a submission submission A minus e m is one was pretty revolutionary a square and other is d equals two into one minus rho, rho is the autocorrelation coefficient. If my d value is two, then the row value is zero. That means there is no correlation d equals to zero means rho equals to one d equals to four means role equals two minus one and if a director statistic lies between 1.5 to 2.5, then we say that there is no autocorrelation.

So, there are two ways to check out the autocorrelation one is you can check using the value of the DDP statistic that is if it lies it happens, notable religion or other is by me checking the p value that is if my h notice is the data does not have a autocorrelation h1 is not correlation exists. So, it may be you is greater than the level of significance which by default in most cases have 5% that is if the p value is greater than 0.05, then I will accept the null hypothesis otherwise they'll reject the null hypothesis for diagnosis. There is no autocorrelation and alternative hypothesis there is autocorrelation. So in this video we'll be doing here. In my next video, I'll be discussing about how to do about the practical application of linear regression or clinical data management in SAS for now, let me end this video over here.

Thank you Goodbye. See what for the next video