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# Regression on Stock Returns

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I need some help with the calculations below:
Estimate a regression of the form given by the below
ri = β0 +β1Si + β2Mβi+ β3PEi+ β4βETAi +Ui
In order to evaluate the effect of various firm -specific factors on the returns of a sample of firms . You run a cross -sectional regression with 200 firms
Where ri= percentage annual return for the stock
Si= is the size of the firm I measured in terms of sales revenue
Mβi= the market to book ratio of the firm
PEi is the price /earnings (P/E) ratio of the firm
ΒETAi is the stock 's CAPM beta coefficient
You obtain the following results (with standard errors in parenthesis)
ri = 0.080 +0.801Si + 0.32Mβi+ 0.164PEi+ 0.084βETAi
(0.064) (0.147) (0.136) (0.420) (0.120)
Calculate the t ratios. What do you conclude about the effect of each variable on the returns of the security? On the basis of your results what variables would you consider deleting from the regression? If a stock's beta increased from 1 to 1.2 what would the expected effect on the stocks return? Is the sign on the beta as you would have expected. Explain your answers in each case.

https://brainmass.com/economics/regression/regression-on-stock-returns-579534

#### Solution Summary

The solution explains the computation of t ratios of a multiple regression model and the identification of significant variable from the t ratios with step-by-step calculations.

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## Regression Equation and Statistical Analysis of Stock Return

The returns from an electronic firm's stock and the corresponding returns for the market portfolio for the past 15 years are given below. (See attached file for better table representation)

Market Return (%) Stock's Return (%)
16.02 21.05
12.17 17.25
11.48 13.1
17.62 18.23
20.01 21.52
14 13.26
13.22 15.84
17.79 22.18
15.46 16.26
8.09 5.64
11 10.55
18.52 17.86
14.05 12.75
8.79 9.13
11.6 13.87

1. Carry out the regression and find the B for the stock. What is the regression equation.
2. Does the value of the slope indicate that the stock is above-average risks?
3. Give a 95% confidence interval for this B. Can we say the risk is above the average 95% confidence?
4. If the market portfolio return for the current year is 10%, what is the stock's return predicted by the regression equation? Give a 95% confidence interval for this prediction.
5. Construct a residual plot. Do the residuals appear random?
6. Construct a normal probability plot. Do the residuals appear to be normally distributed?

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