Question

# A manager at a local bank analyzed the relationship between monthly salary (y, in \$) and...

A manager at a local bank analyzed the relationship between monthly salary (y, in \$) and length of service (x, measured in months) for 30 employees. She estimates the model: Salary = β0 + β1 Service + ε. The following ANOVA table summarizes a portion of the regression results.

 df SS MS F Regression 1 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02 Service 9.19 3.20 2.87 0.01

a) The coefficient of determination indicates that ________.

2. a) Over the past 30 years, the sample standard deviations of the rates of return for stock X and Stock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. When testing whether the correlation coefficient differs from zero, the value of the test statistic is t28 = 2.31. At the 5% significance level, the critical value is t0.025,28 = 2.048. The conclusion to the hypothesis test is ________.

3. a) The following data for five years of the annual returns for two of Vanguard’s mutual funds, the Vanguard Energy Fund (x) and the Vanguard Healthcare Fund (y), were given as sx = 35.77, sy = 13.34, sxy = 447.68. The competing hypotheses are H0: ρxy= 0HA: ρxy ≠ 0H0⁢: ρxy⁢= 0⁢HA⁢: ρxy⁢ ≠ 0⁢⁢ . At the 5% significance level, which of the following is the critical value of the test statistic?

Ans:

1)coefficient of determination indicates,R^2=555420/2518293=0.221 or 22.1%

coefficient of determination indicates that 22.% of the variation in salary is explained by the service.

2)

Test statistic,t=2.31

critical t value=2.048

As,test statistic t is greater than critical t value,we reject the null hypothesis.

There is sufficient evidence evidence to conclude that  the correlation coefficient differs from zero.

3)n=5

df=5-2=3

critical t value=tinv(0.05,3)=3.182

critical r value=0.878