You are considering the relationship between annual returns on the S&P 500 index (January 31 to January 31) and annual changes in the unemployment rate. You define:S = annual % change in the S&P500 (SPX)U = annual % change in the unemployment rateYou consider the following univariate relationship:Si = b0 + b1Ui + εiYou have data on annual changes in the unemployment rate and the S&P500 (SPX) from 2002 through 2020 (19 observations) and you want to use the data to estimate the regression coefficients (intercept b0 and slope b1)You are given the following statistics:StatisticValueCov(U,S)-0.025043Var(U)0.034590E(U)-0.001530E(S)0.064267TSS0.627907RSS0.326368Compute the estimated coefficients for the intercept (b0) and slope (b1) and the R2So far in 2021, the unemployment rate has decreased by 24% (from 6.3 percent to 4.8 percent). If the unemployment rate holds steady until the end of the year, resulting in an annual change of -24% (so U21 = -0.24), what is the expected value of S21 (annual return on the S&P500)?Once you have the forecast value for S21 calculate a 95% confidence interval for your forecast.

Given, The slope of the regression line (b1) can be calculated by dividing the covariance of X and Y…

Answered: You are considering the relationship…

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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Compute the estimated coefficients for the intercept (b₀) and slope (b₁) and the R²
So far in 2021, the unemployment rate has decreased by 24% (from 6.3 percent to 4.8 percent). If the unemployment rate holds steady until the end of the year, resulting in an annual change of -24% (so U₂₁= -0.24), what is the expected value of S₂₁ (annual return on the S&P500)?
Once you have the forecast value for S₂₁ calculate a 95% confidence interval for your forecast.

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