Your task is to apply the Market Model for each stock’s returns and the TSX Index returns
Regression Case
Your task is to apply the Market Model for each stock’s returns and the TSX Index returns. Do a complete regression analysis for each stock, following the analysis steps provided in the study guide and presented in the course materials. Write a report describing the analyses conducted. Your interpretations of the beta coefficient and coefficient of determination should be discussed in terms of the financial model. In your conclusion, provide a summary table of all relevant parameters and discuss which stocks are most and least sensitive to changes in the index. Also explain which stocks’ risk could be diversified by creating an appropriate portfolio. You do not need to develop a portfolio.
Note that the last step "7 If the model fits the data, use the regression equation.” is not directly applicable other than your explanations of sensitivity and risk. This step really applies to using the model for prediction.
You should use the p-value criterion for any hypothesis tests conducted. Use only summary tables within the text of your report. If any data is within your text, it should be something you are discussing!! I do not need to see the raw data anywhere. You can include your Excel output in an Appendix if you like and refer to it there.
The intent of the case is for each student to work through several complete regression analyses (with help from your team for understanding :-)). However, when it comes to the final write up, if you organize it by regression steps (including all 9 stocks’ graphs together or a table in one place) rather than by stock, you can use one summary paragraph to explain the your analysis for each step. This eliminates a lot of the repetition that results when organizing by individual stock. This is less writing for you and less reading for me ;-). It makes my grading easier too and anything you can do to make your professor’s grading easier is always a good thing
Procedure for Regression Diagnostics
1. Develop a model that has a theoretical basis.
2. Gather data for the variables in the model.
3. Draw scatter diagrams for all X,Y to determine whether a linear model appears to be appropriate and check for outliers.
4. Determine the regression equation and residuals.
5. Using the residuals, check the required conditions for the errors and re-check for outliers.
a. Is the error variable normally distributed with a mean of zero? Check for nonnormality
Draw a histogram of the residuals and interpret the shape (Can use Standardized Residuals)
b. Is the error variance constant for all value of x? Check for Heteroscedasticity.
If the variance of the errors is not the same for every value of x, then we have heteroscedasticity. Check this by plotting the residuals against the predicted values of y (with Y on the x-axis) and looking for change in spread of the data points as you move across the x-axis.
c. Are the errors independent? Check for Autocorrelation.
Autocorrelation is when the error terms for different values of y are related to each other in some way. This can be a problem for time-series data (and only needs to be checked for time-series data). Plot the residuals against time periods and look for patterns – Do a line plot of the residuals
d. Check the existence of outliers and influential observations
Look for any standardized residuals that are less than -2 or greater than +2
6. Assess the model fit.
a. Standard Error of the Estimate
Compare to average Y
b. Coefficient of Determination (R2)
Interpret it and evaluate it
c. Test Validity of Model
ANOVA F test
d. Test significance of coefficients and interpret them
t-test of beta
7. If the model fits the data, use the regression equation.
StatisticsRegression analysis is the technique which is widely used for prediction and forecasting. It is basically used to know that dependent variable is related to which independent variable. Linear regression is used to estimate the relationships between variables by fitting an equation to given data. Linear Regression is used to predict the value of y which is dependent on x (explanatory vari...
Regression analysis is the technique which is widely used for prediction and forecasting. It is basically used to know that dependent variable is related to which independent variable. Linear regression is used to estimate the relationships between variables by fitting an equation to given data. Linear Regression is used to predict the value of y which is dependent on x (explanatory variable or independent). If we consider one independent variable it is referred to as Linear Regression. While if we consider more than one independent variable it is referred to as Multiple Linear Regression models.
The equation of Linear Regression is
With a unit increase in Xi there is βi unit increase/decrease in Y
Hypothesis test of Model:
Null Hypothesis: Hoi: Model is not significant. V/s Alternative Hypothesis: H1i: Model is significant. I use F test statistic to test this. If p-value < alpha, I reject Ho at 5% level of significance otherwise I fail to reject it.
The regression model is easy to use and apply but the major limitation is that regression will give correct results only if dependent and independent variables are correlated to each other.
One of the assumptions is regression model should not have multi-co-linearity, which means independent variables will not be correlated to each other
Other assumptions involve there should be no autocorrelation, that is error terms in prediction must not be correlated with each other.
The variance of error terms must be constant, that there should not be heteroscedasticity.
Residuals should be normally distributed.
All these assumptions may not be valid on real-world data which makes it difficult for managers to make a prediction as per regression.