Exam 15: Inference With Regression Models

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. At the 5% significance level,which of the following explanatory variable(s)is(are)individually significant?

A marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model: Sales = β₀ + β₁ Advertising + ε.The following table shows a portion of the regression results. When testing whether the slope coefficient differs from 3,the critical values at the 5% significance level are −2.069 and 2.069.The conclusion to the test is to _______________________________________________.

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether or not x₁ and x₂ have the same influence on y,the null hypothesis is ____________.

The restricted model is a reduced model where we estimate the coefficients that are restricted under the null hypothesis.