9.3 Model Assumptions

In Section 9.2, we assumed that the probabilistic model relating the drug reaction time y to the percentage x of drug in the bloodstream is

y=β0+β1x+ε

We also recall that the least squares estimate of the deterministic component of the model, β0+β1x, is

y^=β^0+β^1x=.1+.7x

Now we turn our attention to the random component ε of the probabilistic model and its relation to the errors in estimating β0 and β1. We will use a probability distribution to characterize the behavior of ε. We will see how the probability distribution of ε determines how well the model describes the relationship between the dependent variable y and the independent variable x.

Step 3 in a regression analysis requires us to specify the probability distribution ...

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