1．ich statement is most accurate? Assume a 5 percent level of significance. The F-statistic is: Analysis of Variance Table (ANOVA) | Source | Degrees of
freedom (df) | Sum of
Squares
| Mean Square
(SS/df)
| F-statistic | Regression | 5 | 18,500 | 3,700 |
| Error | 94 | 600.66 | 6.39 |
| Total | 99 | 19,100.66 |
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A) 579.03 and the regression is said to be statistically significant. B) 0.0017 and the regression is said to be statistically significant. C) 0.0017 and the regression is said to be statistically insignificant. D) 579.03 and the regression is said to be statistically insignificant. The correct answer was A) F =3,700/6.39 = 579.03 which is significant since the critical F value is between 2.29 and 2.37. The critical F value is found by using a 5% level of significance F-table and looking up the value that corresponds with 5 = k = the number of independent variables in the numerator and 100 _ 5 _ 1 = 94 df in the denominator resulting in a critical value between 2.29 and 2.37. 2．regression equation with 4 independent variables is estimated using 20 data points. The R2 is 0.46. An analyst is testing to see whether all of the coefficients are equal to zero. The p-value for the test is: A) lower than 0.025. B) between 0.025 and 0.05. C) between 0.05 and 0.10. D) greater than 0.10. The correct answer was B) To solve this problem, one can assume any value for the total sum of squares. In this case, assume its 1. The regression sum of squares is R2 multiplied by the total sum of squares, which is 0.46. The residual sum of squares is the difference between the total sum of squares and the regression sum of squares, which is 1 − 0.46 = 0.54. The numerator degrees of freedom is equal to the number of independent variables, which is 4, and the mean regression sum of squares is the regression sum of squares divided by the numerator degrees of freedom, which is 0.46 / 4 = 0.115. The denominator degrees of freedom is the number of observations minus the number of independent variables, minus 1, which is 20 − 4 − 1 = 15. The mean squared error is the residual sum of squares divided by the denominator degrees of freedom, which is 0.54 / 15 = 0.036. The F-statistic is the ratio of the mean regression sum of squares to the mean squared error, which is 0.115 / 0.036 = 3.19, which is in between the F-values (with four numerator degrees of freedom and 15 denominator degrees of freedom) of 3.06 for a p-value of 0.05 (calculated using the F-table at 5%) and 3.80 for a p-value of 0.025 (calculated using the F-table at 2.5%). 3．dependent variable is regressed against a single independent variable across 100 observations. The mean squared error is 2.807, and the mean regression sum of squares is 117.9. What is the correlation coefficient between the two variables? A) 0.30. B) 0.99. C) 0.55. D) 0.65. The correct answer was C) The correlation coefficient is the square root of the R2, which can be found by dividing the regression sum of squares by the total sum of squares. The regression sum of squares is the mean regression sum of squares multiplied by the number of independent variables, which is 1, so the regression sum of squares is equal to 117.9. The residual sum of squares is the mean squared error multiplied by the denominator degrees of freedom, which is the number of observations minus the number of independent variables, minus 1, which is equal to 100 − 1 − 1 = 98. The residual sum of squares is then 2.807 × 98 = 275.1. The total sum of squares is the sum of the regression sum of squares and the residual sum of squares, which is 117.9 + 275.1 = 393.0. The R2 = 117.9 / 393.0 = 0.3, so the correlation is the square root of 0.3 = 0.55. 4．study of a sample of incomes (in thousands of dollars) of 35 individuals shows that income is related to age and years of education. The following table shows the regression results: | Coefficient | Standard Error | t-statistic | P-value | Intercept | 5.65 | 1.27 | 4.44 | 0.01 | Age | 0.53 | ? | 1.33 | 0.21 | Years of Education | 2.32 | 0.41 | ? | 0.01 |
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| Anova | df | SS | MS | F | Regression | ? | 215.10 | ? | ? | Error | ? | 115.10 | ? |
| Total | ? | ? |
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The standard error for the coefficient of age and t-statistic for years of education are: A) 0.40; 5.66. B) 0.53; 2.96. C) 0.20; 1.96. D) 0.32; 1.65. The correct answer was A) standard error for the coefficient of age = coeff / t-value = 0.53 / 1.33 = 0.40 t-statistic for the coefficient of education = coefficient / standard error = 2.32 / 0.41 = 5.66 5．an square regression (MSR) and mean square error (MSE) are: A) 102.10; 7.11. B) 107.55; 3.60. C) 7.38; 3.42. D) 6.72; 3.58. The correct answer was B) df for Regression = k = 2 df for Error = n – k – 1 = 35 – 2 – 1 = 32 MSR = RSS/df = 215.10/2 = 107.55 MSE = SSE/df = 115.10/32 = 3.60 | 
发表于 2008-4-1 18:00
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