The REG Procedure Model: model1 Dependent Variable: HOWN HOWN The REG Procedure
ID: 3182838 • Letter: T
Question
The REG Procedure
Model: model1
Dependent Variable: HOWN HOWN
The REG Procedure
Model: model2
Dependent Variable: HOWN HOWN
You are to estimate the following model for the state of Virginia.
Model 1: HOWNi = 1 + 2RINCTHi + ui
Model 2: HOWNi = 1 + 2RINCTHi + 3URi + ui
Where HOWN is the homeownership rate (%), RINCTH is real median household income in thousands of dollars and UR is the unemployment rate (%). The data file has RINC in dollars. You are to write a short SAS program to read in the data file, construct RINCTH in the SAS program (not in Excel), and estimate the two models. Also provide a correlation matrix for the three variables.
1) For model 1, present the estimated model as an equation, including standard errors and R2 and give a written interpretation of the estimate of 2.
2) For model 2, present the estimated model as an equation, including standard errors and R2 and give a written interpretation of the estimate of 2 and of the estimate of 3.
3) In Model 2, does the unemployment rate have statistically significant effect on homeownership? Demonstrate with a formal test using a two-tailed alternative.
4) For Model 2, test the hypothesis that every one percentage point increase in the unemployment rate causes a one percentage point decrease in the homeownership rate against the alternative that the effect is larger (larger magnitude). For this test, draw a diagram to illustrate the p-value for the test. Use Excel to measure it.
5) Given a written interpretation of the R2 for Model 2.
The SAS SystemExplanation / Answer
1) For model 1, present the estimated model as an equation, including standard errors and R2 and give a written interpretation of the estimate of 2.
The model equation is formed using the coeffiecients table for model 1 which is
Hown = 48.95 +0.33*Rinchth
The R2 value for model 1 is 0.2597 , this means that model2 is able to capture 25.97% variation of the data with the fitted regression line
b2 is 0.33 , which means that for a unit change in the value of rinchth , the value of the dependent variable hown woiuld change by 0.33 units
2) For model 2, present the estimated model as an equation, including standard errors and R2 and give a written interpretation of the estimate of 2 and of the estimate of 3.
The model equation is formed using the coeffiecients table for model 2 which is
Hown = 55.49+0.29*Rinchth-1*UR
The R2 value for model 2 is 0.5579 , this means that model2 is able to capture 55.79% variation of the data with the fitted regression line
b2 is 0.29 , which means that for a unit change in the value of rinchth , the value of the dependent variable hown woiuld change by 0.29 units
b3 is 1 , which means that for a unit change(increase in the value of rinchth , the value of the dependent variable hown woiuld change in the opposite direction(decrease) by 1 units
3) In Model 2, does the unemployment rate have statistically significant effect on homeownership? Demonstrate with a formal test using a two-tailed alternative.
as the p value of the UR is less than 0.05 , hence at an alpha of 0.05 , we can conclude that the variable is significant and contributed in explaining the variation of the data
Given a written interpretation of the R2 for Model 2.
The R2 value for model 2 is 0.5579 , this means that model2 is able to capture 55.79% variation of the data with the fitted regression line
Please note that we can answer only 4 subparts of a question at a time, as per the answering guidelines
Parameter Estimates Variable Label DF ParameterEstimate Standard
Error t Value Pr > |t| Intercept Intercept 1 55.49468 5.30110 10.47 <.0001 rincth 1 0.29948 0.08029 3.73 0.0008 UR UR 1 -1.00631 0.22749 -4.42 0.0001# less than 0.05 , hence significant
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