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Econometrics questions.

Econometrics questions.

Find Econometrics university examination questions in acaproso.com

# Question
1

The average duration of unemployment (D) appears to increase when the unemployment rate (U) increases. Data were collected and run to test this hypothesis with regression analysis. Regression results are reported in the table below.

Regression analysis results- STATA.

Source SS df MS   Number of obs 11
        F(1,9) 32.7
Model 62.0025302 1 62.0025302 Prob>F 0.0003
Residual 17.0629282 9 1.89588091 R-Squared 0.7842
Total 79.0654584 10 7.90654584 Adj R-squared 0.7602
        Root MSE 1.3769
d Coef. Std.Err t P>t [95% conf. Interval]
u 2.469684 .4318592 5.72 0.000 1.49275 3.446617
-cons   2.056377 -0.03 0.980 -4.705918 4.597778
  1. Whatsign would you expect for hat{eta_{1}} and hat{eta_{0}} ? Why ?
  2. Are the results in the table above consistent with your priori hypothesis?
  3. What is the mathematical form of this case?
  4. Comment on overall results of the analysis?

Mathematical Calculation
2

Using a sample of 1801 black individuals, the following earnings (E), equation has been estimated.

ln(hat{E}) =7.059 + 0.147 Education + 0.049Experience+0.201 female

(0.135)(0.008)   (0.007)  (0.036)

R^{2}=0.179; n=1801

Where the standard errors are reported in parenthesis.

  1. Using acceptable notations specify an econometric model that was estimated
  2. State all the assumptions underlying the estimation of the econometrics model specified in part (a) along with the problems that will be encountered if the assumptions are relaxed/ violated.
  3. Interpret the coefficient estimate on female.

In Answering part (d), you must write down

  1. The null and alternative hypothesis
  2. The test statistic
  3. The rejection rule
  1. Test the hypothesis that there is no difference in expected earnings between black women and black men. Test this hypothesis against a two-sided alternative, using the 5% significant level.

Mathematical Calculation
3

Two distributions of data are being analyzed. Distribution A has a mean of 500 and a standard deviation equal to 100. Distribution B has a mean of 10 and standard deviation equal to 4. Which of the two distributions has a greater relative variation?


Mathematical Calculation
4

Two distributions have the following characteristics:

Distribution A Distribution B
mu=45,600 mu=33.40
sigma=6,333 sigma=4.05

If a value from distribution A is 50,000 and a value from distribution B is 40, convert each value to a standardized z value and indicate which one is closer to its respective mean.


Mathematical Calculation
5

Using your knowledge ANOVA complete all the missing values in the table below:

Analysis of variance for a simple regression model.

Source of variation Sum of square(SS) Degree of freedom (df) Mean square (MS)=(SS/df) F-statistic
Regression(ESS) 150.75      
Residual (RSS)   8    
Total(TSS) 300.40 9    
  1. Explain why the test statistic used in ANOVA should be F-statistic.
  1. Given this F-test what are numerator`s and denominator`s degree of freedom?

Mathematical Calculation
6

The following are random observations from a certain population : 15,25,35,20,30,65,72,87,89,78,89,98,102,69,56,78,89,56,67,89,90,89,56,90,78,56,98,103,56,79 and 56.

Find

  1. The mean
  2. The mode
  3. The median
  4. The range
  5. The minimum
  6. The maximum
  7. The sample variance
  8. The population variance
  9. The sample standard deviation
  10. The population standard deviation.

Mathematical Calculation
7

The table below shows data on X and Y observed from a certain population

X 1 2 3 4 5
Y 1 1 2 2 4

Given that Y=eta _{0}+eta_{1}X +mu ,

eta _{1} =frac{sum (X- overline{X})((Y- overline{Y}))}{sum (X- overline{X})^{2}}  and eta _{0} =overline{Y}- eta_{1} overline{X}

  1. Calculate the values of eta _{0} and eta _{1}
  2. Find hat{Y}
  3. Find the errors

Mathematical Calculation
8

The following are results obtained from a linear regression model after post estimationof problems that are commonly encountered during the estimation process.

Model summary

Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson
1 976 953 944 4.53138 1.335

Predictors: (Constant), Farm income, Non wage income, Wage income

Dependent Variable Consumption, Expenditure

ANOVA

Model Sum of Squares df Mean Square F Sig

Regression

Residual

Total

6601.311

328.535

6929.846

3

16

19

2200.437

20.533

 

107.164

 

 

.000

 

 

Predictors:(COnstant), Farm income, Non wage income, Wage income.

Dependent Variable: Consumption, expenditure

Coefficients

Model Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics
B Std. Error Beta Tolerance VIF
(Constant) 7.912 8.968   .882 .391    
Wage income 1.056 .173 .920 6.098 .000 .130 7.684
Non wage income .469 .659 .056 .711 .487 .476 2.100
Farm income .128 1.086 .016 .118 .908 .162 6.189
Dependent Variable: Consumption expenditure          

Using your knowledge on linear regression to answer the following questions

  1. Specify a regression model that was estimated and state whether the independent variables are jointly significant (use alpha=1%)
  2. Identify the coefficients of the regression model that are statistically significant at the level of significance of  0.01
  3. What problems were tested during the post estimation? What additional problem should have been tested?
  4. Is there any assumption of the ordinary least square model that was violated ?
  5. What is the best way(s) to deal with this/ these problem(s)?

Mathematical Calculation
9

Y and X are sample data for crop yield and amount of fertilizer applied to the crop respectively

Crop yield(Y) 200 400 600 800 1000
Amount of fertilizer(X) 20 20 40 50 55

Given that Y=eta_{0}+eta_{1}X+mu , hat{eta_{1}}=frac{sum (X-ar{X})(Y-ar{Y})}{sum (X-ar{X})^{2}}, and eta_{0}=ar{Y}-eta_{1}ar{X}

  1. Calculate the estimates of eta_{0}  and eta_{1}
  2. Find hat{Y}_{n} for n=(1,2,3,4,5)
  3. Find the errors
  4. In view of theory on linear regression what is the expected value of errors?
  5. In practice what is the ideal way to test whether the values of the predicted errors are consistent with the theory?

Mathematical Calculation
10
  1. What is confidence interval?
  2. Ready carefullly the data presented in the table below

Coursework grades for students enrolled in statistics at SUA.

Observation No 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Score(%) 30 64 30 29 40 52 67 29 64 37 40 67 29 37
Observation No 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Score(%) 67 29 64 37 64 30 64 30 29 40 52 67 29 64
Observation No 29 30 31                      
Score(%) 37 40 67                      

Using the data presented in table above answer the following questions

  1. Find the sample variance and standard devication of these coursework grades
  2. Find the 95% confidence interval (C.I) for the true mean
  3. Based on this interval test whetehr the mean grade is at least 50%.

Mathematical Calculation