An economist believes that housing construction depends (positively) on household income and (negatively) on interest rates. Having read only the chapter on simple regression, he regresses housing construction on income, ignoring interest rates, and obtains a negative estimate of β, indicating that an increase in household income decreases housing construction. How might his omission of interest rates explain this incorrect sign? Be specific.

His sister, a chemist, proposes a controlled experiment, in which interest rates are held constant, while incomes are varied: “In this way, you will be able to see the effects of income changes on construction.” Why does the economist resist this sisterly advice?