# Maximum Likelihood Estimators with Normally Distributed Error

Maximum Likelihood Estimators with Normally Distributed Error

In statistics, there is a frequent desire to develop a model that has, of all models in that class, the maximum likelihood of producing the data observed. This Demonstration shows how to derive the maximum likelihood estimates of the coefficients in a linear model of data () that is believed to have normally distributed error with a standard deviation of a user-set value . The top panel shows the data, the current regression model (as an orange line) and the probability (likelihood) that each value would occur for a given value, given and . The bottom panel shows the sum of the logs of each of these likelihoods. Selection of maximum likelihood estimates of and will make this sum as large as possible and the displayed rectangle as small as possible. Curious users can request a computation of the maximum likelihood estimate for each dataset.

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