Ordinary least squares
Example with real data

The following data set gives average heights and weights for American women aged 30–39 (source: The World Almanac and Book of Facts, 1975).

When only one dependent variable is being modeled, a scatterplot will suggest the form and strength of the relationship between the dependent variable and regressors. It might also reveal outliers, heteroscedasticity, and other aspects of the data that may complicate the interpretation of a fitted regression model. The scatterplot suggests that the relationship is strong and can be approximated as a quadratic function. OLS can handle non-linear relationships by introducing the regressor HEIGHT. The regression model then becomes a multiple linear model:

The output from most popular statistical packages will look similar to this:

In this table:

Ordinary least squares analysis often includes the use of diagnostic plots designed to detect departures of the data from the assumed form of the model. These are some of the common diagnostic plots:

An important consideration when carrying out statistical inference using regression models is how the data were sampled. In this example, the data are averages rather than measurements on individual women. The fit of the model is very good, but this does not imply that the weight of an individual woman can be predicted with high accuracy based only on her height.
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