invic

A study of 40 men finds that their job satisfaction and marital satisfaction scores have a correlation coefficient of 0.52. At 5% level of significance, is the correlation coefficient significantly different from 0?

A) No, t = 1.68.

B) No, t = 2.02.

C) Yes, t = 3.76.

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H0: r = 0 vs. Ha: r ≠ 0
t = [r √(n – 2)] / √(1 – r2) <P >="[(0.52" √(38)] √(1 – 0.522)="3.76"
tc (α = 0.05 and degrees of freedom = 38) = 2.021
t > tc hence we reject H0.

invic

Suppose the covariance between Y and X is 0.03 and that the variance of Y is 0.04 and the variance of X is 0.12. The sample size is 30. Using a 5% level of significance, which of the following is most accurate? The null hypothesis of:

A) no correlation is rejected.

B) significant correlation is rejected.

C) no correlation is not rejected.

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The correlation coefficient is r = 0.03 / (√0.04 * √0.12) = 0.03 / (0.2000 * 0.3464) = 0.4330.
The test statistic is t = (0.4330 × √28) / √(1 − 0.1875) = 2.2912 / 0.9014 = 2.54.
The critical t-values are ± 2.048. Therefore, we reject the null hypothesis of no correlation.

invic

Consider a sample of 60 observations on variables X and Y in which the correlation is 0.42. If the level of significance is 5%, we:

A) cannot test the significance of the correlation with this information.

B) conclude that there is no significant correlation between X and Y.

C) conclude that there is statistically significant correlation between X and Y.

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The calculated t is t = (0.42 × √58) / √(1-0.42^2) = 3.5246 and the critical t is approximately 2.000. Therefore, we reject the null hypothesis of no correlation.

invic

Consider a sample of 32 observations on variables X and Y in which the correlation is 0.30. If the level of significance is 5%, we:

A) conclude that there is significant correlation between X and Y.

B) conclude that there is no significant correlation between X and Y.

C) cannot test the significance of the correlation with this information.

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The calculated t = (0.30 × √30) / √(1 − 0.09) = 1.72251 and the critical t values are ± 2.042. Therefore, we fail to reject the null hypothesis of no correlation.

invic

Suppose the covariance between Y and X is 10, the variance of Y is 25, and the variance of X is 64. The sample size is 30. Using a 5% level of significance, which of the following statements is most accurate? The null hypothesis of:

A) no correlation is rejected.

B) significant correlation is rejected.

C) no correlation cannot be rejected.

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The correlation coefficient is r = 10 / (5 × 8) = 0.25. The test statistic is t = (0.25 × √28) / √(1 − 0.0625) = 1.3663. The critical t-values are ± 2.048. Therefore, we cannot reject the null hypothesis of no correlation.

invic

The purpose of regression is to:

A) get the largest R2 possible.

B) explain the variation in the dependent variable.

C) explain the variation in the independent variable.

The goal of a regression is to explain the variation in the dependent variable.

invic

The capital asset pricing model is given by: Ri =Rf + Beta ( Rm -Rf) where Rm = expected return on the market, Rf = risk-free market and Ri = expected return on a specific firm. The dependent variable in this model is:

A) Ri.

B) Rm - Rf.

C) Rf.

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The dependent variable is the variable whose variation is explained by the other variables. Here, the variation in Ri is explained by the variation in the other variables, Rf and Rm.

invic

The independent variable in a regression equation is called all of the following EXCEPT:

A) predicted variable.

B) predicting variable.

C) explanatory variable.

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The dependent variable is the predicted variable.

invic

Joe Harris is interested in why the returns on equity differ from one company to another. He chose several company-specific variables to explain the return on equity, including financial leverage and capital expenditures. In his model:

A) return on equity is the independent variable, and financial leverage and capital expenditures are dependent variables

B) return on equity is the dependent variable, and financial leverage and capital expenditures are independent variables.

C) return on equity, financial leverage, and capital expenditures are all independent variables.

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The dependent variable is return on equity. This is what he wants to explain. The variables he uses to do the explaining (i.e., the independent variables) are financial leverage and capital expenditures.

invic

Sera Smith, a research analyst, had a hunch that there was a relationship between the percentage change in a firm’s number of salespeople and the percentage change in the firm’s sales during the following period. Smith ran a regression analysis on a sample of 50 firms, which resulted in a slope of 0.72, an intercept of +0.01, and an R2 value of 0.65. Based on this analysis, if a firm made no changes in the number of sales people, what percentage change in the firm’s sales during the following period does the regression model predict?

A) +1.00%.

B) +0.72%.

C) +0.65%.

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The slope of the regression represents the linear relationship between the independent variable (the percent change in sales people) and the dependent variable, while the intercept represents the predicted value of the dependent variable if the independent variable is equal to zero. In this case, the percentage change in sales is equal to: 0.72(0) + 0.01 = +0.01.