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) 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 rate You consider the following univariate relationship: Si = b0 + b1Ui + εi You 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: Statistic Value Cov(U,S) -0.025043 Var(U) 0.034590 E(U) -0.001530 E(S) 0.064267 TSS 0.627907 RSS 0.326368 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.

) 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 rate You consider the following univariate relationship: Si = b0 + b1Ui + εi You 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: Statistic Value Cov(U,S) -0.025043 Var(U) 0.034590 E(U) -0.001530 E(S) 0.064267 TSS 0.627907 RSS 0.326368 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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  1. ) 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 rate

    You consider the following univariate relationship:
    Si = b0 + b1Ui + εi

    You 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:


Statistic

Value

Cov(U,S)

-0.025043

Var(U)

0.034590

E(U)

-0.001530

E(S)

0.064267

TSS

0.627907

RSS

0.326368
  1. Compute the estimated coefficients for the intercept (b0) and slope (b1) and the R2
  2. 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)?
  3. Once you have the forecast value for S21 calculate a 95% confidence interval for your forecast.

 

 

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