LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BA 18

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – November 2008

ST 5405 – ECONOMETRIC METHODS

 

 

 

Date : 14-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

            PART A

                                                                                                                                                                                                                                                                                                                                              

Answer ALL questions                                                                                                         (10 x 2 = 20)

 

1. Define the term ‘Econometrics’.
2. What is meant by Population regression line?
3. Is the model Y = β₁ + β₂e^X + u linear with respect to X? Why or why not?
4. Interpret the following confidence interval.

                   Pr (-1.5 < β₂ < 2.2) = 0.95, where β₂ is the regression coefficient in a

      two variable linear model.

1. Mention any two properties of OLS estimators.
2. For a two variable linear model, the sample regression function is found to be Y = 1.7 + 4.5X + e. Interpret the regression equation.
3. The observed and predicted values of the dependent variable Y in a linear model is as follows:

                  Observed Y:  14         12        20        14        11

                  Predicted Y:  11         10        18        13        14

      Find the value of R².

1. What is meant by multicollinearity?
2. When are two regression equations said to be parallel and dissimilar?
3. How is the ‘bench mark category’ interpreted in a regression model involving

      dummy independent variables?      

 

 

PART B

 

Answer any FIVE questions                                                                                                            (5 x 8 = 40)

 

11. Explain the concept of ‘Population regression function’ through an example.
12. Mention the assumptions underlying the classical linear regression model.
13. Suppose that a researcher is studying the relationship between grade points on

     exam(Y) and hours studied for the exam(X) for a group of 20 students.   

     Analysis of the data reveals the following:

                 Sum of Y = 1600:      Sum of X = 400

                 Sum of xy = 1800;     sum of x² = 600

Residual sum of squares = 43,200 where x and y are the deviations of X and Y from their respective means.

     Find the following:

• Mean of X and Y
• Least squares intercept and slope
• Standard error of regression
• Standard error of slope coefficient

14. For a two variable linear model, derive the variance of the OLS estimators.
15. Describe the method of testing the overall significance of a regression

             model.

16. Find the residual sum of squares for the following data by assuming a linear

            model of Y on X.

.                       Y: 10          12                         15        17        13

                        X: 1.3         1.5            1.7       2.0       1.6.

17. Explain the various remedial measures available to overcome the problem of multicollinearity. 

 

 

18. Consider the following OLS regression results with standard errors in

parenthesis:

           S = 12,000 – 3000X₁ + 8000(X₁ + X₂)          

                                  (1000)    (3000)                        n = 25

where S = annual salary of economists with B.A. or higher degree

           X₁ = 1 if M.A. is highest degree; 0 otherwise

           X₂ = 1 if Ph.D is highest degree; 0 otherwise

• What is S for economists with a M.A. degree?
• What is S for economists with a Ph.D degree?
• What is the difference in S between M.A.’s and Ph.D’s?
• At 5% level of significance, would you conclude that Ph.D’s earn more per year than M.A.’s?

 

PART C

 

Answer any TWO questions                                                                                                (2 x 20 = 40)

 

19. Consider the following data on Y and X:

                 Y: 2.57    2.50    2.35    2.30    2.25    2.20    2.11    1.94

                 X: 0.77    0.74    0.72    0.73    0.76    0.75    1.08    1.81

      Fit a linear model of Y on X and test the hypothesis that the intercept and 

      slope coefficients are statistically significant at 5 % level.

 

20. ) Explain the method of constructing a 100(1-α) % confidence interval for
    the slope parameter in a two variable regression model.

      b.) What is a ‘k’ variable linear model? Give an example for the same.

      c.) Explain the method of computing r² based on a two variable linear model.

                                                                                                                                                           (10+4+6)

21. a.)  Consider the following ANOVA table based on a linear regression:

                                           Source                 df        Sum of squares

                                           Regression           4          ?

                                           Residual              ?          128

                                           Total                    19        500

                     1.) Find the missing values.

                     2.) Compute the F-ratio and test the hypothesis that R² is significantly

                          different from zero at 5 % level.

                     3.) Write the form of the PRF.

                     4.) Obtain an estimate for the variance of the disturbance term.

 

               b.) Consider the following results based on a linear regression:

                    The estimated regression line is

                                            = 53.428 + 0.895 X₁ – 0.926 X₂         R² = 0.167

                                                   (11.462)  (0.607)       (0.607)           n = 16

                    where the numbers in the parenthesis denote the standard errors.

                    Does the above information reveal the presence of multicollinearity in the

                    sample data? Justify your answer.                                                                              (10+10)

 

22. a.) Consider the following data on annual income (in 000’s $) categorized by gender and age.

                                      Income: 12         10       14     15        6       11       17

                                      Gender:  0            1          1      0         0         1         1

                                                 Age:  1            1          0      1         0         0         1

                   where Gender = 1 if male; 0 if female

                                   Age = 1 if less than or equal to 35; 0 if greater than 35

                      Perform a regression of Income on Gender and age. Interpret the results.

 

               b.) Define Heteroscedasticity. Explain the Spearman’s rank correlation test to detect the      

                     presence of   heteroscdasticity.                                                                                    (10 + 10)

 

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     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 31

FIFTH SEMESTER – April 2009

ST 5405 – ECONOMETRIC METHODS

 

 

 

Date & Time: 30/04/2009 / 1:00 – 4:00  Dept. No.                                                    Max. : 100 Marks

 

 

SECTION A

Answer all questions                                                                         (10 x 2 = 20)

 

1. What is the difference between a ‘Mathematical model’ and an ‘Econometric model’?
2. Define Sample Regression Function.
3. Mention any two properties of OLS estimators.
4. What is meant by ‘Time series’ data? Give an example for the same.
5. Interpret the following regression equation.

Y = 2.5 + 0.21X₁ + 1.0X₂ ,

where Y denotes the weekly sales( in ‘000’s)

X₁ denotes the weekly advertisement expenditure

X₂ denotes the number of sales persons.

1. In a multiple regression model, the value of R² is found to be 0.657. How is it interpreted?
2. For a two variable regression model, the observed and estimated (under OLS) values of Y are given below:

Observed Y:   10         14        13        12        17

Estimated Y:  10         13        11        14        15

Calculate the standard error of the regression.

1. What is meant by ‘dummy variable’?
2. Mention any two methods of overcoming multicollinearity.
3. Define Heteroscedasticity.

 

SECTION B

Answer any five questions                                                                (5 x 8 = 40)

 

1. Explain the various steps involved in an Econometric study.
2. Explain the method of least squares and hence obtain the OLS estimators for the intercept and slope parameters based on a two variable linear model.
3. The following data relates to the family income(X) and expenditure(Y) (both in dollars per week) of 8 families randomly selected from a small urban population.

Y: 40   55   50   70   80   100  90  78

X: 60   65   70   63  120  75    68  52

Assuming there is a linear relationship between Y and X, perform a regression of Y on X and estimate the regression coefficient. Also find an unbiased estimate for the variance of the disturbance term.

1. Consider the following information from a 4 variable regression equation:

Residual sum of squares = 94;

Y = 10,12,14,9,7,8,2,22,4,12.

a.) Find TSS and ESS.

b.) Test the hypothesis that R² = 0 at 5% level.

1. Explain the procedure of obtaining a 100(1-α) % confidence interval for the slope parameter in a two variable linear model.
2. What is meant by ‘structural change’? Explain the Chow test for detecting structural change in a ‘k’ variable model.

 

1. What is meant by dummy variable trap? Explain the methods to overcome it.
2. Consider the following data set:

Sample no.:     1           2          3          4          5

Y:    15         10        14        8          3

X:    1           2          3          4          5

Calculate the standard errors of the intercept and slope coefficients if their OLS

estimates are 17.8 and -2.6 respectively.

 

SECTION C

Answer any two questions                                                                (2 x 20 = 40)

 

1. a.) For a two variable linear model, show that the least squares estimators are
   unbiased.

b.) Mention the various assumptions in a Classical Linear Regression model.

(10 + 10)

20. Consider the following data on annual income (Y) (in 000’s $), total
    experience (X₁) and age (X₂).

Y: 12        10                    14      15       6      11       17

X₁: 8          7          9       10       4       6.5      12

X₂: 32        29        35     33       26     28       39

Perform a regression of Y on X₁ and X₂. Interpret the results. Also test the
hypothesis that all the slope parameters are significantly different from zero at

5% level by constructing the ANOVA table.

21. a.) Consider the following ANOVA table based on an OLS regression

 

Source of Variation	Degrees of Freedom	Sum of Squares
Regression	?	1000
Error	35	?
Total	39	2200

 

1. i)  How many observations are there in the sample?
2. ii) How many independent variables are used in the regression?

iii) Find the missing values in the above table

1. iv) What is the standard error of regression?
2. v) Calculate the value of R²
3. vi) Test the hypothesis H_o : R² = 0 vs H₁ : R² ≠ 0 at  5% level.

b.) What is meant by multicollinearity? Explain its consequences.  (12+8)

22. a) Explain the method of generalized least squares to obtain the estimators of

a linear model in the presence of heteroscedasticity.

b.) Write short notes on:

1.) Disturbance term in a linear model.

2.) Differences between correlation and regression.

3.) Differential intercept coefficient.

4.) Adjusted R².                                                                      (10+10)

 

 

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