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# Correlation & Regression

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1- Refer to the following information to answer Questions A through D.To help gain a better understanding of the relationship between the return on the common stocks of small companies and the return on the S&P 500 Index, you run a simple linear regression to quantify this relationship using the monthly return on small stocks as the dependent variable and the monthly return on the S&P 500 as the independent variable. The results of the regression are:

Coefficient STDError t-value
Intercept: 1.71% 2.95 0.601
Slope: 1.52 0.13 10.073

The t-statistical critical value at the 0.01 significance level = 2.26
Residual error = 19.85
Correlation coefficient = 0.7740
N = 75
F-value = 101.465 on 73 degrees of freedom

(A)- Assuming the historical relationship holds for the future, if the expected return on the S&P 500 over the next period is 3 percent, what is the expected return on small stocks over the same period?

(B)-The percent of the variation in the return on the dependent variable explained by the return on the independent variable for the period under study was?

(C)- The regression statistics indicate at the 0.01 significance level,

a. the slope coefficient (1.52) and the intercept (1.71) are both statistically significant.
b. the slope coefficient (1.52) and the intercept (1.71) are not statistically significant.
c. the slope coefficient (1.52) is not statistically significant, but the intercept (1.71) is statistically significant.
d. the slope coefficient (1.52) is statistically significant, but the intercept (1.71) is not statistically significant.

(D)- The regression statistics indicate that the standard deviation of the difference between the actual returns on small stocks and the estimate of those returns is?

QN2-Based on the following regression data:

N = 50 Coefficients Standard Error
Intercept 0.052 0.175
Slope 1.32 0.108

a- State the null and alternate hypotheses for each regression coefficient.

b- Test each hypothesis at the 0.05 significance level and interpret the results.