Suppose that Yt is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Yt has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let μJan denote the average value of housing starts in January and let μFeb, μMar,. . . . , μDec denote the average values in the other months. Show that the values of μJan, μFeb, . . . , μDec can be estimated from the OLS regression Yt = β0 + β1Febt + β2Mart + . . . .+ β11Dect + ut, where Febt is a binary variable equal to 1 if t February, Mart is a binary variable equal to 1 if t is March, and so forth.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose that Yt is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Yt has a pronounced seasonal pattern; for example, housing starts are low in January and high in June. Let μJan denote the average value of housing starts in January and let μFeb, μMar,. . . . , μDec denote the average values in the other months. Show that the values of μJan, μFeb, . . . , μDec can be estimated from the OLS regression Yt = β0 + β1Febt + β2Mart + . . . .+ β11Dect + ut, where Febt is a binary variable equal to 1 if t February, Mart is a binary variable equal to 1 if t is March, and so forth.
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