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# Multiple Regression Analysis

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A prospective home buyer engaged the services of a consultant to develop a multiple regression model to predict mortgage interest rates by using the yield on long-term treasury bonds and the type of mortgage. There are two types of mortgages that the buyer was considering: variable rate (coded 1) and fixed rate (coded 0). All were 30 year mortgages. Data were collected for 20 mortgages and are presented in the table below.

Mortgage Rate % Treasury Bond Yield % Mortgage Type Mortgage Rate % Treasury Bond Yield % Mortgage Type
6.9 5.85 1 6.95 5.95 1
7.1 6.05 1 8.25 6.9 1
7.5 6.05 1 6.3 6.25 1
7.35 5.35 0 6.65 5.4 0
6.3 3.95 0 7.05 5.3 0
8.2 5.9 0 7.05 7.6 1
7.6 6.2 1 7.15 7.05 1
7.25 6.4 1 6.35 5.05 1
9.15 6.45 0 6.6 5.65 0
4.95 4.3 1 8.9 7.25 0

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.800224
R Square 0.640359
Adjusted R Square 0.598048
Standard Error 0.605622
Observations 20

ANOVA
df SS MS F Significance F
Regression 2 11.10214 5.551071 15.13467 0.000168
Residual 17 6.235233 0.366778
Total 19 17.33738

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2.988741 0.917049 3.259086 0.00462 1.053934 4.923548
Treasury Bond Yield % 0.80199 0.157649 5.087194 9.13E-05 0.46938 1.134601
Mortgage Type -0.96512 0.28665 -3.36691 0.003661 -1.5699 -0.36035
(Economics for Management and Economics, Watson, Billingsley, Croft and Huntsberger, Fifth Edition, 1993, Page 688)

(a) Copy and paste the data from this document to an Excel file. Select Mortgage Rate as the dependent variable and Treasury Bond yield and mortgage type as the independent variables. Conduct multiple regression using Excel. Paste the output report below. Note: Follow the instructions given in module 5 to conduct simple regression. At the step where you specify the input data range, instead of selecting the data for one independent variable, select data for all the independent variables.
(b) Write the equation from the regression output report. If you are using symbols in the equation for the variables, do define the symbols before using the symbols in the equation.
(c) Provide clear and complete interpretation of the coefficients b1 and b2 in the equation. There is no need to interpret b0. Note: Use actual variable names and numbers in answering your question. b1 and b2 are slopes is not sufficient answer.
(d) What is the value of R2 for this model? Do you think that the model does a good job of explaining the variation in wages? Why or why not?
(e) Set up the hypotheses to test whether the model is significant. Is the regression model significant at 0.05 as the level of significance? What does this mean?
(f) Set up the hypotheses to test for each of the regression coefficients individually and perform the test at the 0.05 level of significance.
(g) What average mortgage rate do you predict for mortgages of variable rate type (mortgage type = 1) if the treasury bond yield is 6%. Provide a clear and complete interpretation of the prediction.

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#### Solution Summary

The solution provides step by step method for the calculation of multiple regression model. Formula for the calculation and Interpretations of the results are also included.

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