Simple Linear Regression Models (Statistics Project Sample)

Simple Linear Regression Models
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Overview
This paper aims to investigate the relationship between the 90 day Treasury bill yield (dependent variable) and the independent variable of monthly U.S unemployment rate. This model will use monthly data provided in the chosen U.S Treasury bill variable descriptions and aims to find out whether unemployment has a significant impact on the short term interest rates and whether it gives a useful managerial information regarding the direction of short term interest rates.
The data used is monthly data over a recent U.S. business cycle that includes one recession and periods of economic expansion. The data comes from the Federal Reserve Economic Data (FRED) and can be found at https://fred.stlouisfed.org/graph/?g=10aiP . The study aims to identify whether the selected independent variable has a significant and consistent impact on short-term interest rates and provides useful managerial information. The data used for both model 1 and 2 are provided in the form of mean, standard error, median, mode, standard deviation, kurtosis, range, skewness, sum observations and sum weights. Model 2 will aim to evaluate the term structure hypothesis and find out if it really supports pure expectations or the liquidity preferences.
The second regression model developed using the implied three month forward rate of interest computed by pure expectations (lagged three months) as the independent variable and the 90-day U.S. Treasury bill rate as the dependent variable has the following form: 90-day U.S. Treasury bill rate = β0 + β1 (implied three-month forward rate) + ε where β0 is the intercept, β1 is the slope coefficient, and ε is the error term. To derive the implied three-month forward rate, we use the difference between the six month and three-month Treasury bill rates, assuming that the three-month forward rate is equal to the six-month rate minus the difference. The term structure hypothesis suggests that the slope coefficient in the regression model should be positive, indicating that as the maturity of the Treasury bill increases, so does the interest rate.
MODEL 1
Variables:
* 3 month T-Bill: this is the dependent variable in this study. It serves as the short term, risk free rate or yield that is specific to 90-day U.S. Treasury Bill rate. The measurements are in time period (months). This rate is determined by the market forces such as the demand for U.S. Treasury Bills and demand and supply chain figures.
* Unemployment: This is the independent variable. This is measured in percentages of the U.S. unemployment rates over a period of three months.
Null and Alternative Hypothesis
Null
The null hypothesis of this study tests that unemployment rate in U.S. has no significant impact on the short term interest rates, like the 90-day U.S Treasury bill rate.
Alternative
The alternative test of this study is that the unemployment rate of the United States has a significant impact on the short term (90-day) interest rates. In this case, the directional alternative is not warranted.
The regression Model
For a simple regression model of this study, the following formula should be used;
y = β0 + β1x + ε
Where;
* y = dependent variable (90-day US. Treasury bill yield) or the 3 month T-bill
* x = independent variable (unemployment rate over 3 months)
* β0 = the value of y when x is 0 (the intercept)
* β1 = the change in y for a single unit of x (the slope)
* ε = error term (difference between predicted and actual values).
y = β0 + β1x + ε
y = unemployment
β0 = 4.82926
β1 = -13.1341
Unemployment = (4.82926 + -13.1341)x + ε
3 Month Data
3 month forward rate
Variable description

3 Month

Unemployment 3 month forward

Mean
Median
Minimum
Maximum
Standard deviation
C.V
Skewness
Kurtosis
Range
Sum observations

4.5000
4.5000
4.4000
4.6000
0.1