Suppose \(Y_{t}\) is the monthly value of the number of new home construction projects started in the United States. Because of the weather, \(Y_{t}\) has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let \(\mu_{\text {Jan }}\) denote the average value of housing starts in January, and let \(\mu_{F e b}, \mu_{M a r}, \ldots, \mu_{D e c}\) denote the average values in the other months. Show that the values of \(\mu_{\text {Jan }}, \mu_{F e b}, \ldots, \mu_{D e c}\) can be estimated from the OLS regression \(Y_{t}=\beta_{0}+\beta_{1}\) Feb \(_{t}+\beta_{2}\) Mar \(_{t}+\cdots+\beta_{11}\) Dec \(_{t}+u_{t}\), where \(\mathrm{Fe}_{t}\) is a binary variable equal to 1 if \(t\) is February, \(\mathrm{Mar}_{t}\) is a binary variable equal to 1 if \(t\) is March, and so forth. Show that \(\beta_{0}+\beta_{2}=\mu_{M a r}\) and so forth.