Sage-Tips

What does it mean if observations in a sample are independently and identically distributed?

Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in the sample are taken from the same probability distribution. Independent means that the sample items are all independent events. In other words, they aren’t connected to each other in any way.

Why do we need assumptions in machine learning?

Residuals are used as an indication to how well your model fits to the data. However, to be able to trust and have confidence in the results, there are some assumptions that you must meet prior to modeling. Satisfying all these assumptions would allow you to create the best possible estimates for your model.

Why IID assumption is important?

So in a way the assumption of I.I.D helps simplify training machine learning algorithms by assuming that the data distribution won’t change over time or space and sample wont be dependent on each other in anyway.

What is assumption in machine learning?

It assumes that there is minimal or no multicollinearity among the independent variables. It usually requires a large sample size to predict properly. It assumes the observations to be independent of each other.

Why you should investigate your data to see if it meets the diagnostic assumptions before conducting any data analysis?

As you prepare to conduct your statistics, it is important to consider testing the assumptions that go with your analysis. Assumption testing of your chosen analysis allows you to determine if you can correctly draw conclusions from the results of your analysis.

What does identically distributed mean in probability?

Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in the sample are taken from the same probability distribution. Independent means that the sample items are all independent events.

What does the IID assumption imply about the data?

What i.i.d. assumption states is that random variables are independent and identically distributed. You can formally define what does it mean, but informally it says that all the variables provide the same kind of information independently of each other (you can read also about related exchangeability).

What is the IID assumption?

What are the key assumptions for SLR?

There are four assumptions associated with a linear regression model: Linearity: The relationship between X and the mean of Y is linear. Homoscedasticity: The variance of residual is the same for any value of X. Independence: Observations are independent of each other.