The following is the estimation results for a multiple linear regression model: Y = 0 + 1

Fantastic news! We've Found the answer you've been seeking!

Question:

The following is the estimation results for a multiple linear regression model:

Y = _{0 +}₁X₁+ ₂X₂ +

SUMMARY OUTPUT

Regression Statistics

R-Square 0.677

Standard Error of Regression (S) 803.190

Observations 47

Coeff. Std. Error t-Stat

Intercept 1123.058 317.573 3.536

X₁ 25.121 6.072

X₂ 0.893 0.322

Questions:

Use the fitted model to make a prediction for Y when X₁ = 0.27 and X₂ = 1.39 (Three decimals; 5 points).
Calculate the t-stat for the slope ₁ (Three decimals; 5 points).
Calculate the 95% confidence interval for the slope ₂(Three decimals; 10 points).
Are these two slopes statistically significant at 5% significance level (10 points)?

Problem 2. The following is a multiple linear regression model:

Y = _{0 +}₁X₁+ ₂X₂ +

A portion of the computer analysis obtained from Microsoft Excel 2016 is shown below:

SUMMARY OUTPUT

Regression Statistics

R-Square 0.983

Regression Standard Error 13.519

Observations 56

Coeff. Std. Error t Stat

Intercept 252.70 8.93

X₁ -0.29 0.07

X₂ 0.000059 0.00006

Referring to the table above, what is the interpretation of the R²(5 points)?
Find the sum of squared residuals, SSE, and the sum of the squared difference between the observed dependent variable and its average, SST(Three decimals; 10 points).
Calculate the confidence interval for the slope ₂at the 95% confidence level (Seven decimals; 5 points).
Calculate the t-stat for the slope ₁ (Three decimals; 5 points).
Are these two slopes statistically significant at 5% significance level (10 points)?

Problem 3 (A Real Data Application). Recalling in the simple linear regression model in Module 3, I gave a real data example using the Nobel-winning Capital Asset Pricing Model (CAPM). In that example, we obtained R² = 0.108, or 10.8%, which is a small value way less than 100%. This means that the single independent variable, the market return, R_M, does not explain the return of an individual stock or portfolio very well in this simple linear regression model. Researchers have been developing new methodologies to add other independent variables to better capture the relationship between returns of an individual asset and the measures of these independent variables. Fama and French (1992) [1] develop a three-factor model by adding two other variables on the basis of the CAPM.

The model is in a form of: R = + ₁R_M + ₂SMB + ₃HML₊

where R is the returns of an individual financial asset (i.e. a stock or a portfolio), R_Mis the market return (such as the S&P 500's return as we used in the CAPM), SMB is the Small (market capitalization) Minus Big, and the HML is the High (book-to-market ratio) Minus Low. Here R_M, SMB, and HML are the three factors. This is a typical multiple linear regression model.

This three-factor model can be used in the mutual fund industry to explain the return of an individual asset by the three factors. I have uploaded one real data set in EXCEL into the Homework Assignment#4 area in Canvas. Please download the data file to work on the following question. In the file, we look at a famous mutual fund called Fidelity Megellan fund. It is a monthly data spanning from January of 1979 to January of 2006.

Question: Using EXCEL, please run the estimation procedure for the above-mentioned three-factor model and illustrate your findings/comments based on the estimation of the model. Please specially pay attention to the R²(35 points). Please attach your EXCEL file for the model estimation results.