Model allows us to estimate response distribution at any X
Bivariate data sets contain response measurements corresponding to a few specific values of X, whereas a normal linear model provides a response distribution for all X. By fitting a normal linear model to the data, it is therefore possible to estimate the response distribution at x-values for which we do not have data.
Compressive strength of concrete
The data set below arose from experiments that were performed to assess how the compressive strength of concrete is affected by its curing time. Five samples of concrete of the same composition were mixed. The compressive strength (mPa) of one sample was measured after each of 2, 7, 14, 21 and 28 days. (Testing is destructive, so different samples were needed for each curing period.)
Curing period (days) | Compressive strength (mPa) | ||
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The relationship of strength to curing period is expected to be linear, so we will try to fit a normal linear model to the data. The least squares line is shown in the diagram below with the grey band representing ± twice the estimate of σ.
Drag the slider to display the estimated normal distribution of the compressive strength after any curing period.
The mean of this estimated distribution (i.e. the least squares line) provides a prediction of the compressive strength of a different sample of concrete, after any curing period.