# Dynamic Regression A Simulation Exercise - Math Problem Example

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The equation of the form rjt = j + jrmt + Ujt where rjt represent the stock returns, rmt represents the market return and Ujt represents other factors that influence stock return, this model states that the return of a stock depend on the market return. We consider the Motorola stock returns MOTOR and the general public utilities GPU stock return in this case and consider the returns over time, the following chart shows their returns and also the market return:

## Extract of sample "Dynamic Regression A Simulation Exercise"

Download file to see previous pages From the chart it is also the drop is also evident in the market and MOTOR returns and this shows that a drop in the market returns will also signify a drop in the returns of the stocks in the market. Finally from the chart it is evident that there was a decline in the market returns in 1987 showing that returns for the other stocks also declined.
We use 120 0bservations to estimate the model estimate the model rjt = j + jrmt + Ujt for both stocks, we use MOTOR return data for the year 1976 to 1985, after estimation sung the TSM software the results show that rjt = 0.00255 + 0.7193 rmt
the above model means that is we hold all factors constant and the market return level is equal to zero then the MOTOR stock return will be 0.00255, also if we hold all factors constant and we increase the market return level by one unit then the MOTOR stock return level will increase by 0.7193 units. ...
The above model means that is we hold all factors constant and the market return level is equal to zero then the GPU stock return will be 0.00063, also if we hold all factors constant and we increase the market return level by one unit then the GPU stock return level will increase by 0.4297 units. The R squared for this model is 0.0854and this means that 8.54% of deviations in the dependent variable are explained by the independent variable. The correlation of determination R squared value for this model depicts a weak relationship between the explanatory variable and the dependent variable.
Hypothesis testing:
We test hypothesis for the estimated coefficients in the two models,
MOTOR model:
rjt = 0.00255 + 0.7193 rmt
MOTOR model Constant:
Null hypothesis: = 0
Alternative hypothesis 0
Standard error: 0.00737
Coefficient: 0.00255
T calculated = 0.00255 / 0.00737 = 0.34599
T critical at 95% level of test = 1.95996
When the T calculated value is less than the T critical value we accept the null hypothesis, in the above case therefore we accept the null hypothesis that = 0 and therefore the constant is not statistically significant at 95% level of test.
Motor Model Slope:
Null hypothesis: = 1
Alternative hypothesis: 1
Standard error: 0.12481
Coefficient: 0.7193
T calculated = 1- 0.7193/ 0.12481= 2.249
T critical at 95% level of test = 1.95996
When the T calculated value is greater than the T critical value we reject the null hypothesis, in the above case therefore we reject the null hypothesis that = 0 and therefore the constant is statistically significant at 95% level of test.
GPU model:
rjt = 0.00063 + 0.4297 rmt
GPU model Constant:
Null hypothesis: = 0
Alternative hypothesis 0
Standard error: 0.00841
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