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Kapie

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发表于 2011-7-11 19:04 | 只看该作者

Mid-afternoon snack (quant)

received, following, difficult, job
Sorry that the tables are a little difficult to read. I'll post answers after 4:30 EST.

Keyser S?ze, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and the then asked several questions about regression analysis. Some of S?ze’s questions, along with a sample of the answers he received to each, are given below. S?ze told the applicants that the independent variable is the ratio of net income to sales for restaurants with a market cap more than $100 million and the dependent variable is the ratio of cash flow from operations to sales for those restaurants. Which of the choices provided is the best answer to each of S?ze’s questions?

Regression Statistics:
Multiple R >> 0.8623
R-squared >> 0.7436
Standard error >> 0.732
Observations >> 24


ANOVA: Df ; SS ; MSS ; F ; Significance F
Regression: 1 ; 0.029 ; 0.029000 ; 63.81 ; 0
Residual: 22 ; 0.010 ; 0.000455
Total: 23 ; 0.040


Coefficients ; Standard Error ; t-Statistic ; p-Value
Intercept: 0.077 ; 0.007 ; 11.328 ; 0
Slope: 0.826 ; 0.103 ; 7.988 ; 0

17. What is the value of the coefficient of determination?

A. 0.8261.
B. 0.7436.
C. 0.8623.

18. Suppose that you deleted several of the observations that had small residual values. If you re-estimated the regression equation using this reduced sample, what would likely happen to the standard error of the estimate and the R-Squared?

Standard Error of the Estimate ; R-Squared
A. Decrease ; Decrease
B. Decrease ; Increase
C. Increase ; Decrease


19. What is the correlation between X and Y?

A. –0.7436.
B. 0.7436.
C. 0.8623.

20. Where did the F-value in the ANOVA table come from?

A. You look up the F-value in a table. The F depends on the numerator and the denominator degrees of freedom.
B. Divide the “Mean Square” for the regression by the “Mean Square” of the residuals.
C. The F-value is equal to the reciprocal of the t-value for the slope coefficient.

21. If the ratio of net income to sales for a restaurant is 5 percent, what is the predicted ratio of cash flow from operations to sales?

A. 0.007 + 0.103(5.0) = 0.524
B. 0.077 – 0.826(5.0) = –4.054
C. 0.077 + 0.826(5.0) = 4.207

22. Is the relationship between the ratio of cash flow to operations and the ratio of net income to sales significant at the 5 percent level?

A. No, because the R-squared is greater than 0.05.
B. No, because the p-values of the intercept and slope are less than 0.05.
C. Yes, because the p-values for F and t for the slope coefficient are less than 0.05.
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needhelp1700

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2#
发表于 2011-7-11 19:04 | 只看该作者
Nice ...

17. B is correct. The coefficient of determination is the same as the R-squared.

18. C is correct. Deleting observations with small residuals will degrade the strength of the regression, resulting in an increase in the standard error and a decrease in the R-squared.

19. C is correct. For a regression with one independent variable, the correlation is the same as the Multiple R with the sign of the slope coefficient. Because the slope coefficient is positive, the correlation is 0.8623.

20. B is correct. This answer describes the calculation of the F-statistic.

21. C is correct. To make a prediction using the regression model, multiply the slope coefficient by the forecast of the independent variable and add the result to the intercept.

22. C is correct. The p-value reflects the strength of the relationship between the two variables. In this case the p-value is less than 0.05, and thus the regression of the ratio of cash flow from operations to sales on the ratio of net income to sales is significant at the 5 percent level.

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benbenxiong

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3#
发表于 2011-7-11 19:04 | 只看该作者
Please help - I don't understand #18:

-The first part I get - when you delete small residuals SSE gets only slightly smaller but (n-2) gets much smaller. Since SEE = (SSE/(n-2))^(1/2), SEE INCREASES. Got it.

-The second part I don't understand. If SSE gets slightly smaller because some small residuals were deleted, wouldn't that mean that R^2 would need to get bigger by the following equation:

R^2 = (TSS-SSE)/TSS ???

Help?

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Houjichasan

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4#
发表于 2011-7-11 19:04 | 只看该作者
Good question - fairly basic with some tricks. It would be better if :

Multiple R was not given, (what is multiple r anyways - it is not a term defined in SS3).

For 19, choice B should be same value as Choice c (but with a negative sign). since correlation r = sqrt of r-squared (for a simple linear regression). Also, the sign of the slope coefficient comes into picture since both choice B and C would have satisfied the sqrt equation.

For 22, choice C is appropriate because F and t statistics mean the same thing for a simple linear regresssion. The answer does not say that - even though it correctly defines p-value as the decision criteria for statistical significance.

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