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The LINER model

Checking conditions with the LINER model is to assure that our regression model meet the conditions for making inference.


The LINER model is for checking conditions

As described in Inference about regression, it makes sense to test our estimated regression line in order to consider if it the relationship between X and Y is strong enough to make inferences.

Before making inference, we need to make sure that the conditions for this are met. The “LINER” model lists the conditions for inference about regression:

The Liner Model


The LINER model explained

‘L’ is for Linear and means that there must be a linear relationship between X and Y.

‘I’ is for Independence. Each observation in our sample is independent of each other, so we could be sampling with replacement and/or our sample (n) could be at least 10 times smaller than the size of the population (N) => N > 10n

‘N’ is for Normal. It says that for any X value observed in our sample the Y values must be normally distributed, which can be visualized like this:

The Liner Model_Normally distributed Y for any X observed


‘E’ is for Equal variance and means that, for any X value observed in our sample, the distribution for the correspondent Y values must have the same variance. This is also known as homoscedastic. For example, this example would not work, as one of the Y distributions has a different variance:

The Liner Model_Equal variances_homoscedastic


‘R’ is for Random and means that the data must come from a random sample and/ or from a well-designed randomized experiment.

Meeting these constraints, we can make inferences about our regression analysis trough hypothesis testing for regression analysis and confidence intervals for the slope of the regression line.


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Carsten Grube

Carsten Grube

Freelance Data Analyst


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