# In regression modeling, for tests about regression parameters, df = n – number

*QUESTION:*

In regression modeling, for tests about regression parameters, df = n – number of parameters in the equation for the mean.

a. Explain why df = n – 2 for the model μy = α + βx.

b. Chapter 8 discussed how to estimate a single mean μ. Treating this as the parameter in a simpler regression model, µ_{y} = μ, with a single parameter, explain why df = n – 1 for inference about a single mean.

*ANSWER:*

a. df = n – the number of parameters; for the model, µ_{y} = α + βx, there are two parameters α and β, and so df = n – 2.

b. When the inference is about a single mean, there is only one parameter, and therefore, df = n – 1.

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