## Fox Module 20: Collinearity HW

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NEAS
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Fox Module 20: Collinearity

(The attached PDF file has better formatting.)

Homework assignment: Interest rates and inflation

Financial economists often model nominal interest rates as expected inflation plus the real interest rate plus an error term.

Real interest rates are relatively steady over time.

Expected inflation is often modeled as actual inflation in the previous period.

The error term is both random fluctuation and changes in monetary policy.

A statistician has monthly data for interest rates, wage inflation, and general inflation.

A.     What is the estimated â for a regression of interest rates on general inflation?

B.     What is the standard error of the â coefficient?

C.    What is the estimated â for a regression of interest rates on wage inflation?

D.    What is the standard error of the â coefficient?

E.     What are the estimated â s for a regression of interest rates on both inflation rates?

F.     What is the correlation of wage inflation with general inflation?

G.    What are the standard errors of the â coefficients?

 Month Wage Inflation General Inflation Interest Rates Month Wage Inflation General Inflation Interest Rates January 6.06% 5.12% 7.85% July 6.48% 5.70% 8.39% February 6.18% 5.20% 8.39% August 6.76% 5.60% 8.84% March 6.17% 5.14% 8.17% September 6.74% 5.73% 9.11% April 6.26% 5.35% 8.20% October 7.00% 5.97% 9.04% May 6.40% 5.36% 8.25% November 6.95% 6.00% 8.95% June 6.42% 5.51% 8.25% December 7.28% 6.14% 9.60%

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Moots1
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Can we use excel to do the regression? (This question also applies to the different time we needed to regress without it being said that we could use excel)

[NEAS: Yes]

horshack
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For Part F did anyone get the correlation to equal .96459?

And for Part G did anyone get the SE(Bwage)=.49 and SE(Bgeneral)=.54?

bubba gump
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I agree with part G, but I got .9153 for part F.
rcoffman
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I got that the correlation was also .9646 for part F, and checked my answer in Excel.
PMActuary
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When we talk about correlation do we mean R or R Squared?

The correlation coefficient is defined as just R in the book but there seems to be some disagreement in this post.

I used R = Sq Root (RegSS/TSS) = Sq Root (.000263/.000287) = Sq Root (.9153) = .9567

Thanks!

Forum Guru

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PMActuary, I haven't been able to finish this assignment yet b/c I don't have Excel at home, but I don't think R (or R^2) is the correct correlation here. Part F asks for the correlation between X1 and X2; it does not ask for the correlation coefficient.

In a simple regression, R is the correlation between X and Y. In a multiple regression, R is the multiple correlation of all the Xs and the Y. "The multiple correlation is also interpretable as the simple correlation between the fitted and observed Y values" (p.93).

I hope that helps.

joop
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Ax
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I agree with CalLadyQED. The correlation of wage inflation with general inflation is Rj^2, not the R^2 in the regression output (which is the correlation between the interest rate and BOTH the wage and general inflation). I got Rj = .930426.
Romas
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Correlation is R, not R squared.
Taking square root of 0.9304 you get 0.965.
You can also check with Excel function CORREL(array1;array2) and compare it with the regression output.

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