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 t_{28} = 2.31. At the 5% significance level, the critical value is t_{0.025,28} = 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 s_{x} = 35.77, s_{y} = 13.34, s_{xy} = 447.68. The competing hypotheses are H0: ρxy= 0HA: ρxy ≠ 0H0: ρxy= 0HA: 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
Get Answers For Free
Most questions answered within 1 hours.