1. Consider a bivariate regression model:

y_i = ₀ + ₁x_1i + _i

(a) When you were exploring the data, you produced a scatterplot of yi against x1i. For low values of x1i, the realisations of yi were very close to the regression line, whereas for larger values of x1i, the spread of yi increased considerably. What do we call the issue described here? Will this affect your esimate of 1? What can you do to resolve this problem?

(b) A colleague suggests that you add two more variables (x_2i and x_3i) to your model. She thinks that the correct model specifi- cation for the project you are workingon should be:

y_i = ₀ + ₁x_1i + ₂x_2i + ₃x_3i + _i

You disagree. Work through the steps you would taketo test whether or not your colleague was right to include x_2i and x_3i.