LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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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)
- Define the term ‘Econometrics’.
- What is meant by Population regression line?
- Is the model Y = β1 + β2eX + u linear with respect to X? Why or why not?
- 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.
- Mention any two properties of OLS estimators.
- For a two variable linear model, the sample regression function is found to be Y = 1.7 + 4.5X + e. Interpret the regression equation.
- 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.
- What is meant by multicollinearity?
- When are two regression equations said to be parallel and dissimilar?
- 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)
- Explain the concept of ‘Population regression function’ through an example.
- Mention the assumptions underlying the classical linear regression model.
- 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
- For a two variable linear model, derive the variance of the OLS estimators.
- Describe the method of testing the overall significance of a regression
model.
- 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.
- Explain the various remedial measures available to overcome the problem of multicollinearity.
- 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)
- 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.
- ) 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)
- 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)
- 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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