Economics Quiz Paper
統計學 HW7
選擇題(每題 5 分，共 105 分)
繳交日期:6.3.2011
1. Economic periods of prosperity followed by recession are described as: A. Secular trend B. Seasonal variation C. Cyclical variation D. Erratic variation 2. The following linear trend equation was developed for annual sales from 1995 to 2001 with 1995 the base or zero year. = 500 + 60t (in $thousands). What are the estimated sales for 2005 (in $thousands)? A. $500 B. $560 C. $1,040 D. $1,100 3. Which one of the following is not a component of a time series? A. Secular trend B. Moving average C. Seasonal variation D. Irregular variation E. All of the above are components 4. The possible values for the Durbin-Watson statistic are A. any value B. any value greater than zero C. any value from 0 …show more content…
to 4 inclusive D. any value less than zero. 5. A question has these possible choices—excellent, very good, good, fair and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results? A. 0 B. 2 C. 4 D. 5
6. What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? A. 3.841 B. 5.991 C. 7.815 D. 11.070 7. What is our decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079? A. The difference is probably due to sampling error; do not reject the null hypothesis B. Not due to chance; reject the null hypothesis C. Not due to chance; do not reject the alternate hypothesis D. Too close; reserve judgment 8. The chi-square distribution is A. positively skewed. B. negatively skewed. C. normally distributed. D. negatively or positively skewed. 9. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution? A. 3 degrees B. 12 degrees C. 15 degrees D. All would 10. If the Durbin-Watson statistic has a value close to 0 or 4, which assumption is violated? A. Normality of the errors B. Homoscedasticity C. Independence of errors D. None of the above 11. Consider the model where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme
The resulting least squares prediction equation is is the response line (equation) for E(y) when x2 = 0 and x3 = 1? A. C. = 16.3 + 2.3x1 = 18.6 + 2.3x1 B. D. = 18.1 + 2.3x1 = 16.3 + 4.1x1
What
12. Consider the interaction model line relating E(y) and x1 when x2 = 2. A. 1 B. 10 C. 16 D. 13
.
Find the slope of the
13. Which of the following is considered one of the most common concerns with time-series data? A. Specification bias B. Multicollinearity C. Serial correlation D. Heteroscedasticity 14. A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model
E(y) = + x +
This model was fit to data collected for a sample of 32 clocks sold at auction; the resulting estimate of β1 was -.31. Interpret this estimate of β1. A. We estimate the auction price will increase $.31 for each additional bidder at the auction. B. β1 is a shift parameter that has no practical interpretation. C. We estimate the auction price will decrease $.31 for each additional bidder at the auction. D. We estimate the auction price will be -$.31 when there are no bidders at the auction. 15. Fast food chains are closely watching what proposed legislation will do to consumption of "huge-sized meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge-sized meals" for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years. Propose a straight-line model that includes both a long-term trend and seasonal component for the time series. For all models, let t = the year in which the data was collected (t = 1, 2, ... , 25), and let variables used to model a seasonal effect. A. E(Y) = 1t C. E(Y) = + D. E(Y) = + B. E(Y) = + t+ + + + + t , , , and be qualitative
16.
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 2006 to 2008. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2006. Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. 16-1. The best interpretation of the constant 3.37 in the regression equation is: A. the fitted value for the first quarter of 2006, after to seasonal adjustment, is 103.37. B. the fitted value for the first quarter of 2006, prior to seasonal adjustment, is log10 3.37. C. the fitted value for the first quarter of 2006, prior to seasonal adjustment, is 103.37. D. the fitted value for the first quarter of 2006, after to seasonal adjustment, is log10 3.37. 16-2. The best interpretation of the coefficient of X (0.117) in the regression equation is: A. the quarterly compound growth rate in contracts is around 11.7%. B. the quarterly compound growth rate in contracts is around 30.92%. C. the annual compound growth rate in contracts is around 30.92%. D. the annual compound growth rate in contracts is around …show more content…
11.7%. 16-3. The best interpretation of the coefficient of Q3 (0.617) in the regression equation is: A. the number of contracts in the third quarter of a year is approximately 314% higher than the average over all 4 quarters. B. the number of contracts in the third quarter of a year is approximately 314% higher than it would be during the fourth quarter. C. the number of contracts in the third quarter of a year is approximately 62% higher than the average over all 4 quarters. D. the number of contracts in the third quarter of a year is approximately 62% higher than it would be during the fourth quarter.
16-4.
To obtain a forecast for the first quarter of 2009 using the model, which of the following sets of values should be used in the regression equation? A. X = 12, Q1 = 0, Q2 = 0, Q3 = 0 B. X = 13, Q1 = 0, Q2 = 0, Q3 = 0 C. X = 13, Q1 = 1, Q2 = 0, Q3 = 0 D. X = 12, Q1 = 1, Q2 = 0, Q3 = 0 16-5.To obtain a forecast for the fourth quarter of 2009 using the model, which of the following sets of values should be used in the regression equation? A. X = 16, Q1 = 1, Q2 = 0, Q3 = 0 B. X = 16, Q1 = 0, Q2 = 0, Q3 = 0 C. X = 15, Q1 = 1, Q2 = 0, Q3 = 0 D. X = 15, Q1 = 0, Q2 = 0, Q3 = 0 16-6. Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2009? A. 133352 B. 421697 C. 49091 D. 1482518 Note. The derivation of chi-squared statistic (approximation) Let O1 ~ b(n, p1 ), where 0 p1 1. According to the Central Limit Theorem, O1 np1 d Z N(0,1) np1 (1 p1
)
2 Z 2 is approximately 2 (1). If we let O2 n O1 and p2 1 p1, we see that
2
(O1 np1 )2 (O1 np1 )2 (O1 np1 )2 (O1 np1 )2 (n O2 np1 )2 np1 (1 p1 ) np1 n(1 p1 ) np1 n(1 p1 )
(O1 np1 )2 [n(1 p1 ) O2 ]2 (O1 np1 )2 (O2 np2 )2 np1 n(1 p1 ) np1 np2 (Ok npk )2 2 (Ok Ek )2 npk Ek k1 k1
2
選擇題(每題 5 分，共 105 分)
繳交日期:6.3.2011
1. Economic periods of prosperity followed by recession are described as: A. Secular trend B. Seasonal variation C. Cyclical variation D. Erratic variation 2. The following linear trend equation was developed for annual sales from 1995 to 2001 with 1995 the base or zero year. = 500 + 60t (in $thousands). What are the estimated sales for 2005 (in $thousands)? A. $500 B. $560 C. $1,040 D. $1,100 3. Which one of the following is not a component of a time series? A. Secular trend B. Moving average C. Seasonal variation D. Irregular variation E. All of the above are components 4. The possible values for the Durbin-Watson statistic are A. any value B. any value greater than zero C. any value from 0 …show more content…
to 4 inclusive D. any value less than zero. 5. A question has these possible choices—excellent, very good, good, fair and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results? A. 0 B. 2 C. 4 D. 5
6. What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? A. 3.841 B. 5.991 C. 7.815 D. 11.070 7. What is our decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079? A. The difference is probably due to sampling error; do not reject the null hypothesis B. Not due to chance; reject the null hypothesis C. Not due to chance; do not reject the alternate hypothesis D. Too close; reserve judgment 8. The chi-square distribution is A. positively skewed. B. negatively skewed. C. normally distributed. D. negatively or positively skewed. 9. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution? A. 3 degrees B. 12 degrees C. 15 degrees D. All would 10. If the Durbin-Watson statistic has a value close to 0 or 4, which assumption is violated? A. Normality of the errors B. Homoscedasticity C. Independence of errors D. None of the above 11. Consider the model where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme
The resulting least squares prediction equation is is the response line (equation) for E(y) when x2 = 0 and x3 = 1? A. C. = 16.3 + 2.3x1 = 18.6 + 2.3x1 B. D. = 18.1 + 2.3x1 = 16.3 + 4.1x1
What
12. Consider the interaction model line relating E(y) and x1 when x2 = 2. A. 1 B. 10 C. 16 D. 13
.
Find the slope of the
13. Which of the following is considered one of the most common concerns with time-series data? A. Specification bias B. Multicollinearity C. Serial correlation D. Heteroscedasticity 14. A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model
E(y) = + x +
This model was fit to data collected for a sample of 32 clocks sold at auction; the resulting estimate of β1 was -.31. Interpret this estimate of β1. A. We estimate the auction price will increase $.31 for each additional bidder at the auction. B. β1 is a shift parameter that has no practical interpretation. C. We estimate the auction price will decrease $.31 for each additional bidder at the auction. D. We estimate the auction price will be -$.31 when there are no bidders at the auction. 15. Fast food chains are closely watching what proposed legislation will do to consumption of "huge-sized meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge-sized meals" for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years. Propose a straight-line model that includes both a long-term trend and seasonal component for the time series. For all models, let t = the year in which the data was collected (t = 1, 2, ... , 25), and let variables used to model a seasonal effect. A. E(Y) = 1t C. E(Y) = + D. E(Y) = + B. E(Y) = + t+ + + + + t , , , and be qualitative
16.
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 2006 to 2008. The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q1 + 1.28 Q2 + 0.617 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2006. Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. 16-1. The best interpretation of the constant 3.37 in the regression equation is: A. the fitted value for the first quarter of 2006, after to seasonal adjustment, is 103.37. B. the fitted value for the first quarter of 2006, prior to seasonal adjustment, is log10 3.37. C. the fitted value for the first quarter of 2006, prior to seasonal adjustment, is 103.37. D. the fitted value for the first quarter of 2006, after to seasonal adjustment, is log10 3.37. 16-2. The best interpretation of the coefficient of X (0.117) in the regression equation is: A. the quarterly compound growth rate in contracts is around 11.7%. B. the quarterly compound growth rate in contracts is around 30.92%. C. the annual compound growth rate in contracts is around 30.92%. D. the annual compound growth rate in contracts is around …show more content…
11.7%. 16-3. The best interpretation of the coefficient of Q3 (0.617) in the regression equation is: A. the number of contracts in the third quarter of a year is approximately 314% higher than the average over all 4 quarters. B. the number of contracts in the third quarter of a year is approximately 314% higher than it would be during the fourth quarter. C. the number of contracts in the third quarter of a year is approximately 62% higher than the average over all 4 quarters. D. the number of contracts in the third quarter of a year is approximately 62% higher than it would be during the fourth quarter.
16-4.
To obtain a forecast for the first quarter of 2009 using the model, which of the following sets of values should be used in the regression equation? A. X = 12, Q1 = 0, Q2 = 0, Q3 = 0 B. X = 13, Q1 = 0, Q2 = 0, Q3 = 0 C. X = 13, Q1 = 1, Q2 = 0, Q3 = 0 D. X = 12, Q1 = 1, Q2 = 0, Q3 = 0 16-5.To obtain a forecast for the fourth quarter of 2009 using the model, which of the following sets of values should be used in the regression equation? A. X = 16, Q1 = 1, Q2 = 0, Q3 = 0 B. X = 16, Q1 = 0, Q2 = 0, Q3 = 0 C. X = 15, Q1 = 1, Q2 = 0, Q3 = 0 D. X = 15, Q1 = 0, Q2 = 0, Q3 = 0 16-6. Using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 2009? A. 133352 B. 421697 C. 49091 D. 1482518 Note. The derivation of chi-squared statistic (approximation) Let O1 ~ b(n, p1 ), where 0 p1 1. According to the Central Limit Theorem, O1 np1 d Z N(0,1) np1 (1 p1
)
2 Z 2 is approximately 2 (1). If we let O2 n O1 and p2 1 p1, we see that
2
(O1 np1 )2 (O1 np1 )2 (O1 np1 )2 (O1 np1 )2 (n O2 np1 )2 np1 (1 p1 ) np1 n(1 p1 ) np1 n(1 p1 )
(O1 np1 )2 [n(1 p1 ) O2 ]2 (O1 np1 )2 (O2 np2 )2 np1 n(1 p1 ) np1 np2 (Ok npk )2 2 (Ok Ek )2 npk Ek k1 k1
2