 # Statistical Analysis Questions

## Question

I'm trying to study the relation between processing time of a task and several independent variables. I do suspect that there is an issue with one of the independent variables which is [the user], I suspect that there is a big variance in processing time when change between users A, B, C or D.

To summarize, we have:
1 Dependent Variable: task Processing time (measured in Number of hours)
4 Independent Variables: System used (System A or B), Location (Local or International), user (User A, B, C or D), Complexity of the job (0 to 5 ....where 0 is not complex and 5 is very complex)

The question that my design should help to answer is:
Do we have a big variability across processing time if we change people (users). In other words, If we control for all other independent variables and vary the users, do we see big variability in the outcome ?

So considering the above, what statistical approach need to be used for analysis with details please ? How can we demonstrate statistical significance with details?

Kindly include equations to be used, any hypothesis, and when to accept and reject a hypothesis.

Please note that what is significant here is the Design of the analysis!

## Solution Preview

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The ordinary least squares estimation method obtains the very ideal coefficient estimates in the multivariate linear regression if required assumptions are satisfied. One of the assumption to obtain the ideal estimates is the constant variance of random error terms. Our present application is suspected to violate this assumption as D2 may have some impact on the conditional variance of the errors. Fortunately, the violation of the constant conditional (on explanatory variables) variance of error terms only makes the estimates less efficient while it preserves the property of unbiasedness.

Nevertheless, performing a test to check whether the model suffers from the violation of the assumption helps us modify the experiment to obtain better model to explain the behavior of processing time in the future....

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