In this assumption, it is assumed that the model is linear in the slope coefficients and the associated error term in the equation. What this means is that the slope in a given linear equation is a number that it is neither squared or it is not a reciprocal for example. It is a number that once graphed within the context of the regression equation will ultimately produce a straight line. The same applies to the error term in this instance.
Always remember that a regression model only needs to be linear in the slope coefficients (parameters) to produce a straight line. Even if the associated variables are squared or cubed for example, as long as the slope coefficients are linear, the line of best fit will plot as a straight line.
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