Christelle Badillo Case 3

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Christelle Badillo Case 3 – Simple Linear Regression Application Introduction Market Model is used as an application in finance in order to minimize the risks when it comes to investing. There are different statistical techniques to limit or minimize risks when it comes to markets. In order to analyze the relationship between two variables, we can use a simple linear regression analysis. In this case, we want to identify whether the stock prices (y) are dependent on the TSE index (x). Scatterplots Figure 1 – TSE Index vs Barrick

Figure 2 – TSE Index vs BMO Figure 3 - TSE Index vs ENB In the three scatterplots, it is clear that there is a positive relationship between TSE and the different stocks. By visual inspection, there is no reason to suspect that there is curdling in the relationship between any of the stocks and the TSE Index. TSE vs BMO shows the strongest positive relationship, and TSE vs Barrick shows a positive relationship with a steady increasing trend, and TSE index vs ENB shows an increasing trend, but has more scattered data. The scatterplots can also identify the different outliers in each of the stocks. For the Barrick stock, we can see that there are numerous outliers, both on the positive values and negative values, specifically 0.36, 0.297, and -0.33 and -0.31. Majority of the data falls within

the -0.2 and 0.2 for Barrick stock. Looking at the BMO scatterplot, it shows a positive linear relationship with some outliers like -0.103 and -0.063. Majority of the BMO’s data points are not scattered and shows an increasing trend that as TSE index increases, the BMO stock increases. Like the Barrick and the BMO stocks, the ENB stock also show an increase trend, however, its data are more closely grouped together and not as spread out. There are outliers such as -0.0887 and -0.143, and 0.138 and 0.128. Regression Equation Table 1: Barrick Regression For the Barrick regression equation, stock= -0.00995 + 1.588(TSE Index) which indicates the for every 1 unit of increase for the TSE Index, there is a 1.588 increase in the Barrick stock prices. BMO

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For the BMO regression equation, BMO stock = 0.0091 + 0.759(TSE Index) which indicates the for every 1 unit of increase for the TSE Index, there is a 0.759 increase in the BMO stock prices. ENB Looking at the ENB, the regression equation, the b 1 =0.231, the y-intercept is 0.0124, and the regression equation is stock price=0.0124 + 0.231(TSE index) which indicates that for every 1 unit increase of stock index, there is a 0.231 increase in ENB stock prices. Residual Analysis Barrick’s residual histogram

Testing for Barrick’s heteroscedascity Testing for autocorrelation Barrick’s residual histogram shows that the data is normal, and is not skewed to any particular direction, nor is it bimodal. There is homoscedasticity which indicates that majority of the data are in equal distance from each other. There is no autocorrelation between the data as shown in the third figure. However, looking at the data points for the. Barrick’s standard residuals, there are two data points that are outside +2 and -2 which are considered as outliers.

BMO’s residual histogram Testing for heteroscedascity Testing for autocorrelation BMO’s residual histogram shows that the data is somewhat normal, but is kind of skewed because an outlier data, but the data is not bimodal. There is homoscedasticity which indicates that majority of the data are in equal distance from each other. There is no autocorrelation between the data as shown in the third figure. However, looking at the data points for the.

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BMO’s standard residuals, there are three data points that are outside +2 and -2 which are considered as outliers. ENB’s residual histogram Testing for heteroscedascity Testing for autocorrelation

ENB’s residual histogram shows that the data is normal, not skewed on either way, and the histogram shows that it is not bimodal. There is homoscedasticity which indicates that majority of the data are in equal distance from each other. There is no autocorrelation between the data as shown in the third figure. However, looking at the data points for the. ENB’s standard residuals, there are two data points that are outside +2 and -2 which are considered as outliers. Model Assessment, Beta, and R 2 Assessing the model fit needs to be completed through three steps: standard error of estimate, coefficient of determination, and testing the slope. Standard error of Barrick is 0.119 is large compared to -0.01080 average of Barrick. Looking at the R 2 0.124, which indicates that approximately 12.4% of the variability stock prices are due to the changes in TSE Index. In order to assess the hypothesis, we are going to conduct a t-test of β where H 0 : β 1 = 0, H a : β 1 Is not equal to 0 with an alpha of 0.05 with the rejection region of p <0.05, since p-value is 0.005, we reject the null hypothesis. There is enough evidence to conclude that β 1 Is not equal to 0 so there is a relationship between stock price of Barrick and the TSE index. Standard error of BMO is 0.027 is large compared to 0.00870 average of BMO stock. Looking at the R 2 0.373, which indicates that approximately 37.3% of the variability stock prices are due to the changes in TSE Index.

In order to assess the hypothesis, we are going to conduct a t-test of β where H 0 : β 1 = 0, H a : β 1 Is not equal to 0 with an alpha of 0.05 with the rejection region of p <0.05, since p-value is 2.25x10 -7 , we reject the null hypothesis. There is enough evidence to conclude that β 1 Is not equal to 0 so there is a relationship between stock price of BMO and the TSE index. Standard error of ENB is 0.0473 is large compared to 0.01225 average of ENB stock. Looking at the R 2 0.0185, which indicates that approximately 1.85% of the variability stock prices are due to the changes in TSE Index. In order to assess the hypothesis, we are going to conduct a t-test of β where H 0 : β 1 = 0, H a : β 1 Is not equal to 0 with an alpha of 0.05 with the rejection region of p <0.05, since p-value is 0.3006, we accept the null hypothesis. There is not enough evidence to conclude that β 1 Is not equal to 0 so there is no relationship between stock price of ENB and the TSE index. Discussion and Conclusion Based on the data, we can use regression analysis to limit the risks for investing in stock. We can see that for the Barrick stock and the BMO stock, there is enough evidence to conclude that there is a relationship between the TSE index which means that financial advisors or people who are working in the stock market can use the TSE Index to identify if market is going to increase or decrease. Looking at the BMO, approximately 37.3% of the variability stock prices are due to the changes in TSE Index which indicates the depending on how volatile the TSE index is, the more that BMO stock is going to change. Hence, because of the 37.3% variability, the BMO stock would benefit the most from diversification. However, for the ENB stock, it can be seen that there is not enough evidence to indicate that there is a relationship between the TSE Index and the changes in ENB stock. This can also be accounted by the standard error which large compared to the average of the ENB stock. Therefore, it is safe to say that the people who are working in the stock market can minimize the risk by not using TSE index to predict the ENB stock.

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A regression analysis is able to identify these risks and conclude when we can use the TSE index in minimizing the risk involved in the market model. This is one technique that can be used when it comes to investing and financial analysts can be used to understand market behavior and identifying which market will be more volatile compared to the other.

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