Regression Model Explaining the Excess Returns of the US Manufacturing Index

MULTIPLE REGRESSION PROJECT REPORT
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(Total words =2943)
Table of Contents 1.0 Executive Summary. 3 2.0 Introduction. 4 3.0 Theoretical Framework. 4 4.0 Economy and Econometric Theory. 5 5.0 Data. 6 6.0 Regression Analysis. 7 6.1 Result Interpretation. 8 7.0 Assumptions Testing. 10 7.1 Normality. 10 7.2 Multicollinearity. 11 7.3 Heteroskedasticity. 12 7.4 Autocorrelation. 14 Reference List 15
1.0 Executive Summary
An empirical analysis utilizing annual data for the US manufacturing index's gross returns, excess market returns, small-minus-big, high-minus-low, robust-minus-weak, conservative-minus-aggressive, and risk-free rate was conducted to identify the relationship between these variables using the R-Studio software. The multiple regression output showed that the independent variables (Mkt.RF, HML, RMW, CMA, RF) together explain 86.37% of the variation in the stock market return of the US manufacturing index's gross returns, after adjusting for the number of independent variables. Post-tests conducted to confirm the reliability of the model showed that the model met the Gauss-Markov assumptions.
2.0 Introduction
The project aims to develop a regression model to explain the excess returns of the US manufacturing index, which is one of the main industry indices categorized by the four-digit Standard Industrial Classification (SIC) codes. The analysis will utilize annual data for the US manufacturing index's gross returns, excess market returns, small-minus-big, high-minus-low, robust-minus-weak, conservative-minus-aggressive, and risk-free rate (Fama and French 2017). The question of interest is to identify the relationship between these variables and the excess returns of the US manufacturing index and to develop a reliable and accurate model that can explain the variability in the index returns.
3.0 Theoretical Framework
Several economic theories suggest potential relationships of interest in the current analysis. The Capital Asset Pricing Model (CAPM) suggests that the excess market returns should have a positive relationship with the excess returns of the US manufacturing index (Rossi 2016; Galagedera 2007). According to CAPM, the market risk premium is the key driver of expected returns, and the excess returns of an individual asset are expected to be positively related to the excess returns of the market (Cahart 1997; Elbannan 2015; Fama and French 2004; Perold 2004;). Therefore, a positive coefficient for the excess market returns variable in the regression model is expected.
The Fama-French Three-Factor Model suggests that the excess returns of the US manufacturing index are also influenced by other factors such as small-minus-big (SMB), high-minus-low (HML), robust-minus-weak (RMW), and conservative-minus-aggressive (CMA). SMB captures the size effect in the stock market, as small-cap stocks tend to outperform large-cap stocks (Fama & French 1993; 2015; 2017). HML captures the value effect, as value stocks tend to outperform growth stocks. RMW captures the profitability effect, as companies with high profitability tend to outperform those with low profitability (Fama & French 1993; 2015; 2017). Finally, CMA captures the investment style effect, as...