# STATS 2015 Multiple Choice Questions

August 30, 2017

Question
Directions: Blacken the letter corresponding to the best answer on your scantron (2.5 points each).

1. If Y = 4 + 11X the slope of the line equals:

a. X

b. 14

c. 11

d. 4

2. In the regression equation Y = a + bX where a = -2 and b = 5 the relationship can be said to be:

a. inverse because b 0

c. indeterminate since a 0

d. meaningless since a < 0

3. If we determine that the correlation between X and Y is statistically significant we can conclude:

a. that X did not cause Y to occur

b. that X caused Y to occur

c. there may be a causal relationship between X and Y

d. that Y caused X to occur

4. Pamela Stones is interested in determining whether weight gains of sheep are independent of the type of feed they receive. This is an example of:

a. a two way ANOVA test of factor design

b. a Chi-square test on weight versus feed

c. a regression analysis of weight gain on number of months in each field

d. none of the above

5. A coefficient of multiple determination of .45 for the regression Y = a + b1X1 + b2X2 + e means that:

a. 20.25 percent of the variation in Y is accounted for in terms of variation in X1 and X2

b. 45 percent of the variation in Y is not accounted for in terms of variation in X1 and X2

c. 45 percent of the variation in Y is accounted for in terms of variation in X1 and X2

d. 55 percent of the variation in Y is accounted for in terms of variation in X1 and X2

6. The chi-square technique of hypothesis testing can be used

a. to conduct goodness-of-fit tests

b. to test the alleged independence of two quantitative variables

c. to make inferences about homogeneity

d. for all of the above purposes (and more)

7. In the time series forecasting, the most important characteristic of amodel is

a. the quality of the fit

b. the amount of multicollinearity in the data

c. the amount of money you get paid to produce it

d. the amount of autocorrelation in the data

8. In simple regression analysis, the sum of the squares for the regression is called

a. the explained variation for Y

b. the error sum of squares

c. the total variation of Y

d. the unexplained variation for Y

9. If you wanted to identify the range in which a regression coefficient should fall with 90% assurance, the analysis that you should perform is called a(n):

a. Goldfeld-Quant test

b. Chi-square goodness of fit test

c. Confidence interval

d. Regression involving cross-sectional data

10. The "least squares method" can be described as:

a. a method of fitting a line to a set of points such that the absolute values of deviations are minimized

b. {S(Y – X)}2

c. S(X – X)2

d. a method of fitting a line to a set of points such that the squared deviations are minimized

11. A CPI Index Number value of 212.34 for 2013 implies that there has been ________ inflation since the base year of 1983.

a. 6.17%

b. 100%

b. 12.34%

d. 112.34%

12. When a contingency table is based on a Chi Square test of independence case, the number of degrees of freedom is the number of rows:

a. times the number of columns

b. minus one times the number of columns

c. minus one times the number of columns minus one

d. times the number of columns minus one

13. All of the following are reasons for obtaining a trend line except

a. we wish to eliminate trend movements from a time series so we can study the other component of the series

b. we are interested in studying the historical depiction of trend

c. we are interested in using the trend line to predict future data

d. we are interested in analyzing relationships between troughs and peaks

14. If we want to change the magnitude of a time series we simply:

a. divide each number into the data set by 100

b. multiply the slope and intercept by 4

c. divide the slope by the number of periods of data each year

d. divide the slope and intercept by the number of periods of data each year

15. In the equation: Yc = 31 + 4.2X1 + 3.5X2:

a. Yc = 38.7 if X1 + X2 = 0

b. Yc increases by 31 for every 1 unit increased in X1 and X2

c. Yc decreases by 3.5 if X2 decreases by 1 unit

d. Yc increases by 4.2 if X1 decreases by 1 unit and X2 is unchanged

16. The method of least squares (void of econometric problems) produces estimated regression coefficients (such as a and b) that are, with respect to the true regression coefficients (such asa &b),

a. unbiased estimators

b. efficient estimators

c. the best linear estimators

d. all of the above

17. In multiple regression analysis, according to a widely used rule of thumb, a parameter estimate b is significant at the 95 percent level of confidence as long as the associated p value

a. is equal to or greater than the parameter

b. is positive

c. is zero or positive

d. is less than .05

18. A sample coefficient of multiple determination, R2, that is close to zero indicates

a. a near-perfect fit of the regression plane to the data

b. an extremely bad fit of the regression plane to the data

c. neither (a) nor (b), because such a coefficient must be close to -1 or +1

d. the regression sum of squares exceeds the total sum of squares

19. One assumption of regression analysis concerns the statistical independence of different sample errors, but this assumption is often violated when the analysis employs

a. dummy variables

b. the step-down method

c. a correlation matrix

d. time-series data

20. Multicollinearity refers to:

a. a condition in which the independent variables are highly correlated with one another

b. the fact that for any values of X1 and X2, the standard errors are the same

c. the fact that a value of a time series may be calculated with its value at some other time period

d. the relationship between the predictor variables and the independent variables

21. Homoscedasticity refer to:

a. the assumption that values of the Y variable are independent of one another

b. the necessity of the normality assumption

c. the fact that the Y values are conditional upon corresponding X values

d. the assumption that all the error terms have about the same standard deviation

22. In the following regression equation a logarithmic transformation was applied to the dependent variable Y: ln(y) = 2.07 + 0.55 ln(x)

A one percent change in x implies that the average value of y increases by:

a. 2.07

b. -7.92

c. .55%

d. 2.07%

23. The easiest way to cure a serious multicollinearity problem in a multiple regression involves

a. regressing each of the independent variables against all of the others and noting whether any of the resultant R2 values lies close to 1

b. setting up a simple correlation matrix and noting any possible correlation between any one independent variable with all of the others as a group

c. dropping one of the highly collinear variables from the regression, although this causes the model to be misspecified .

d. performing an analysis of residuals

24. The trend equation Y = 14 + 3X + 2X2 : (for X = 0,1,2,…)

a. is an example of an exponential trend equation

b. will at first increase and then decrease

c. will at first decrease and then increase

d. is an example of a linear trend equation

25. If independent variables that were uncorrelated with the dependent variable were added to the regression equation, the coefficient of multiple determination would ___________, while the adjusted coefficient of determination would ________________ .

a. decrease, increase

b. decrease, remain the same

c. remain the same, fall

d. increase, decrease

e. increase, increase

26. In the United States, the unemployment rate must be

d. adjusted in all of the above ways

27. In a macroeconomic forecasting model over time:

a. autocorrelation is unlikely

b. simultaneous equation bias is likely

c. autocorrelation is likely

d. both b and c

28. Presented below is an ANOVA table:

Source d.f. SS MS F

Regression 3 246

Error 4 78

Total 7 324

a. The F value is 4.2

b. The Mean Square for the regression is 82

c. The Mean Square for the errors is 19.5

d. All of the above are true

29. The primary role of a statistician is to

a. interpret data using the best techniques

b. interpret data correctly

c. interpret data quickly

d. interpret data at the lowest price

e. get paid as much as he/she can to do as little as possible

30. Given the annual data 200, 250, 300, 350, the first two components of a 3-year centered moving-averages series are

a. 200, 300

b. 200, 250

c. 275, 325

d. 250, 300

31. The Durbin-Watson test is designed to detect

a. covariance

b. multicollinearity

c. autocorrelation

d. specification error

32. Cyclical variation:

a. refers to periodic up and down movements in a time series that tends to occur over long periods of time

b. cannot be accurately measured

c. is invariably positive over any length of time

d. refers to variation in the data that tend to recur during a period of one year or less

33. In a naive model over 120 observations with a time-trend and seasonal dummy variable the estimated coefficients are:

Yt = 1.03 + 0.34t + 4.32 WINTER + 1.62 SPRING + 3.78 SUMMER

(0.03) (1.12) (1.09) (1.20)

where the standard error of the slope coefficients are shown in parentheses under each item (remember that a t = coefficient/ standard error). At the 5% significance level there is not enough evidence to reject the null hypothesis that:

a. the average level of Y is the same between spring and fall

b. the average level of Y differs between winter and summer

c. the average level of Y is the same between summer and fall

d. the average level of Y differs between spring and summer

34. The results of a polynomial trend equation were y = 6.833 – 0.429x + 2.524×2, with n = 8. The x values were coded so that x = 0 in 1992. The estimated value of y for 2002 is:

a. 6.833

b. 254.943

c. -4.29

d. 252.400

e. 992.127

35. The upsurge in retail sales in the fall of each year is an example of:

a. the irregular component.

b. the trend component.

c. the seasonal component.

d. the cyclical component.

e. the disaster component.

36. The graph on the board implies:

SKIP

37. Given the following list of residuals:

time residual time residual

1 -5.6 11 -11.7

2 -2.9 12 -16.5

3 -5.5 13 -17.0

4 -10.5 14 -22.0

5 -8.5 15 -21.0

6 22.6 16 9.0

7 19.4 17 7.1

8 16.5 18 7.5

9 15.2 19 5.2

10 12.0 20 6.5

the pattern suggests:

a. multicollinearity is present.

b. heteroscedasticity is present.

c. autocorrelation is present.

d. homoscedasticity is present.

38. A wage contract calls for a wage increase to include one-half of the annual percentage increase (if any) in the Consumer Price Index. In 2002 the CPI equaled 124.0 and in 2003 equaled 130.7. The wage percentage increase equaled:

a. 2.70

b. 5.40

c. 6.70

d. 3.35

e. 0.50

39. A leading publication lists the average gross weekly earnings in 2013 as \$385.09. The report also lists the average gross weekly earnings in constant dollars with 1999 = 100, as \$208.42. Find the index value used to adjust average gross weekly earnings. The index value is:

a. 164.8

b. 100.0

c. 159.0

d. 169.8

e. 184.8

40. The best time for you to have taken this course was:

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