Question

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 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⁢= 0⁢HA⁢: ρxy⁢ ≠ 0⁢⁢ . At the 5% significance level, which of the following is the critical value of the test statistic?

Answer 1

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