Simple leaner regression - Statistics Project Example

Question In the CAPM model, B0 is the risk free rate of return and its value is expected to be positive (usually the Treasury bill). The slope, B1,is the beta coefficient in CAPM model and measures the volatility of an asset’s return compared to that of the overall market. The benchmark value is 1.0 (perfect slope). The value can be more than 1.0 to show that a stock is more responsive to market changes or simply riskier than the market. The value can be less than 1.0 which indicates that the stock is less responsive to market changes (or is less risky).

Question 2The plotted trajectories of x and y are shown in the chart below. As shown, a positive linear relationship between the two variables is expected. Question 3Obsyxy2χ2yχ=0+1χɛ = y - 1 3.32 0.72 11.02 0.52 2.39 1.34 1.98 2 1.40 1.68 1.96 2.82 2.35 2.12 - 0.72 3 0.65 - 0.72 0.42 0.52 - 0.

47 0.19 0.46 4 0.93 0.81 0.86 0.66 0.75 1.42 - 0.49 5- 1.21 - 0.35 1.46 0.12 0.42 0.49 - 1.70 6- 1.62 - 2.30 2.62 5.29 3.73 - 1.08 - 0.54 7 1.41 0.80 1.99 0.64 1.13 1.41 0.

00 8 0.18 0.40 0.03 0.16 0.07 1.09 - 0.91 9 1.88 - 0.65 3.53 0.42 - 1.22 0.24 1.64 10 1.35 0.39 1.82 0.15 0.53 1.08 0.27 Total 8.29 0.78 25.74 11.30 9.68 8.29 - Completed table obsYXSQYSQXYXY_HATE13.320.7211.022400.5184002.3904001.3554651.96453521.401.681.9600002.8224002.3520002.091122-0.69112230.65-0.720.4225000.518400-0.4680000.2519790.39802140.930.810.8649000.6561000.7533001.424433-0.4944335-1.21-0.351.4641000.1225000.4235000.535513-1.7455136-1.62-2.302.6244005.2900003.726000-0.958791-0.66120971.410.801.9881000.6400001.1280001.416770-0.00677080.180.400.0324000.1600000.0720001.110246-0.93024691.88-0.653.5344000.422500-1.2220000.3056201.574380101.350.391.8225000.1521000.5265001.1025830.247417Eviews Summary Descriptive ResultsYXSQXSQYYXY_HATE Mean 0.829000 0.078000 1.130240 2.573570 0.968170 0.863494-0.

034494 Std. Dev. 1.447730 1.117615 1.659833 3.141602 1.482091 0.856439 1.136141 Sum 8.290000 0.780000 11.30240 25.73570 9.681700 8.634939-0.344939 Sum Sq. Dev. 18.86329 11.24156 24.79541 88.82698 19.76935 6.601388 11.61734 Observations 10 10 10 10 10 10 10Question 4The slope (β0) = (0.620455)(1.45)/(1.12) = 0.804The intercept (β1) = 0.83 – (1.01)(0.08) = 0.766. Question 5SSR = Sum of (Predicted y – population mean of y)^2 = 6.6132 SSR Mean 0.661329 Median 0.

305059 Maximum 3.196195 Minimum 0.074847 Std. Dev. 0.994800 Skewness 1.938750 Kurtosis 5.352234 Jarque-Bera 8.570002 Probability 0.013774 Sum 6.613286 Sum Sq. Dev. 8.906647 Observations 10Question 6Variance of returns, σ2 = 2.10 Standard deviation of returns, y, σ = 1.45Standard deviation, x = 1.12 Question 7The slope is 0.804 and the p-value is 0.056. At 5% level of significance, the slope is not significantly different from zero. The intercept is 0.766 and the p-value is 0.079. At 5% level, the intercept is not significantly different from zero.

VariableCoefficientStd. Errort-StatisticProb.  C0.7663100.3818442.0068650.0797X0.8037210.3591712.2377140.0556R-squared0.384964    Mean dependent var0.829000Adjusted R-squared0.308084    S.D. dependent var1.447730S.E. of regression1.204243    Akaike info criterion3.386435Sum squared resid11.60160    Schwarz criterion3.446952Log likelihood-14.93218    Hannan-Quinn criter.3.320048F-statistic5.007366    Durbin-Watson stat1.877887Prob(F-statistic)0.055623Question 8Testing whether the slope, 0.

804, is bigger or lower than 1 is a one-tailed t-test. Since the calculated t-statistic is below the rejection level, we cannot reject the null hypothesis that the slope is significantly lower than 1. The stock is not more volatile than the market. Wald Test:Equation: EQ_CAPM_REGTest StatisticValuedfProbabilityt-statistic-0.612004 8 0.5575F-statistic 0.374549(1, 8) 0.5575Chi-square 0.374549 1 0.5405Null Hypothesis: C(1) = 1Null Hypothesis Summary:Normalized Restriction (= 0)ValueStd. Err.-1 + C(1)-0.233690 0.381844Restrictions are linear in coefficients.

Question 9SSE = 11.60 SST = SSE + SSR = 11.60 + 7.26 = 18.86Question 10Correlation coefficient = 0.62 (Excel I21)Coefficient of determination, r2 = 0.622 = 0.38Question 11Done and tables pasted in the questions above.