Simple Regression Analysis

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Seth Hill
Professor Gwinn
Econometrics
March 3, 2011
Unemployment Rate and Total New Houses Sold

For decades, owning a home has been touted as the very heart of "the American Dream", but today that dream is out of reach for an increasing number of Americans. Why? It is because there are not nearly enough jobs for everyone. Without a jobs recovery, there simply is not going to be a housing recovery. In this report, I will perform a regression analysis to determine the effect of the Unemployment Rate (UR) on Total New Houses Sold (TNHS). I expect that there will be a negative relationship between the two variables. In other words, as the unemployment rate increases, the total number of new houses sold will decrease.

The simple functional form of the model is TNHS=f(UR), where TNHS (measured in thousands) is the dependent variable and UR (16 years and over) is the explanatory variable. To determine the relationship between the two variables, one must set up the Population Regression Function (PRF). The PRF represents the regression line of the population as a whole. The deterministic PRF for the model is E(TNHSt|UR) = B₁ + B₂URt. B1 and B2 are population parameters. B₁ is the intercept coefficient and represents TNHS when UR is zero. In regression analysis, the population regression function is estimated on the basis of the sample regression function (SRF). That is, the PRF is an estimator of the SRF. The deterministic SRF in this case is TNHS = b1 + b2UR. In this function, b1 and b2 are estimators for B1 and B2 in the PRF. The PRF and SRF functions in their stochastic forms are: PRF:TNHSt = B1 + B2URt + Ut

SRFTNHSt = b1 + b2URt + et
In the PRF, Ut is the population error term. The population error term is a random variable that cannot be explained by the PRF. This term represents the difference between the actual value of TNHS and the value predicted by the regression equation. In other words, the error term accounts for variables that affect TNHS...
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