Least squares
In practical situations, the three parameters of the normal linear model, β0, β1 and σ, are unknown values — all that we have available is a single data set that we believe comes from a model of this form. Although we cannot hope to determine the values of these unknown parameters exactly, we can obtain estimates of them from the data.
The best estimates of β0 and β1 are the slope and intercept of the least squares line, b0 and b1
Zinc in aquatic plants and lake sediment
Variability of the least squares slope and intercept
Since b0 and b1 are functions of a data set that we assume to be a random sample from the normal linear model, b0 and b1 are themselves random quantities — they would be different if a different data set was collected.
The sample-to-sample variability of the least squares estimates means that the least squares slope and intercept in the aquatic zinc data are unlikely to be exactly equal to the underlying β0 and β1.