LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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B.A. DEGREE EXAMINATION – ECONOMICS
FOURTH SEMESTER – APRIL 2007
ST 4204 – ECONOMETRICS
Date & Time: 19/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A
Answer all questions. (2*10=20)
- Define the term ‘Econometrics’.
- What are mutually exclusive and exhaustive events?
- Let P(A) = 0.3; P(BC) = 0.4; P(A|B) = 0.54. Find P(A∩B).
- Consider the following distribution function of X:
X: -2 -1 1 2
P[X=x]: 0.25 0.5 0.13 0.12
Find E(2X+3).
- Give any two properties of normal distribution.
- Define: null and alternative hypothesis.
- Show that the observed mean and estimated mean of Y for a simple linear model of Y on X are equal.
- Obtain ESS from the following data given that RSS = 133.
Y: 10 14 17 20 25 30 19 27
- What is Variance Inflating Factor? When will its value be equal to one?
- Mention the limitations of OLS estimates in the presence of heteroscedasticity?
SECTION B
Answer any FIVE questions. (5*8=40)
- Explain the concept of population regression function and sample regression
function with an example.
- A family consists of 4 boys and 4 girls. If 3 among them are selected at
random, what is the probability that a.) all are girls b.) exactly 2 are boys
c.) first and last are girls and middle one is a boy.
- Fit a binomial distribution to the following data:
X: 0 1 2 3 4
Frequency: 7 10 8 4 1
- a.) What is a standard normal distribution?
b.) Let X be a normally distributed random variable with mean 24 and
variance 9. Find the percentage of observations i.) above 10 ii.) between
22 and 25.
- What is meant by structural change? Explain the procedure of Chow’s test to
test for the presence of structural change.
- What are dummy variables? Explain its usefulness in regression analysis with
example.
- Consider the following regression result:
Estimate Standard Error T-Ratio
Constant 10.325 2.147 ?
Intercept 5.12 ? 13.56
Slope -7.16 1.45 ?
ANOVA TABLE
Source df Sum of Squares
Regressors 2 ?
Error ? 122
Total 22 348
- Find the missing values.
- Find R2 and test the overall significance of the model at 5% level.
- Explain the method of Generalized Least Squares to estimate the regression
parameters in the presence of heteroscedasticity.
SECTION C
Answer any TWO questions. (2*20=40)
- Five families live in an apartment. The number of cats each family keeps as
pets are indicated in the following table:
Family: 1 2 3 4 5
Number of cats: 0 4 0 0 6
- What is the “mean number of cats” for the population of families?
- Suppose that a researcher took a random sample of two families. What is the sample mean number of cats for each of the 10 possible samples?
- Calculate the frequency and relative frequency of each possible value of the mean number of cats for all samples of size two and give the sampling distribution.
- What are the mean and variance of this sampling distribution?
- Suppose that the researcher took a random sample of four families. What is the sample mean number of cats for each of the 5 possible samples?
- Calculate the frequency and relative frequency of each possible value of the mean number of cats for all samples of size four and give the sampling distribution.
- What is the mean and variance of this sampling distribution?
- Is the mean of the samples an unbiased estimator of the population mean for samples of sizes two and four?
- What conclusion can be drawn about the variance of the sampling distribution as the sample size increases?
- Suppose that a researcher is studying the relationship between gallons of milk
consumed by a family per month (Y) and the price of milk each month ( X in
dollars per gallon). The sample consists of observations in 12 consecutive
months. Analysis of the data reveals the following:
∑ Y = 480 ∑ X = 36 ∑ xy = -440
∑ x2 = 20 RSS = 528
where x and y are the deviations of X and Y from their respective means.
- Find the least squares intercept and slope.
- Find the standard error of the slope.
- Test whether the slope is significantly different from zero at 5% level.
- Assume that the Total Sum of Squares (TSS) is 1100. Form an ANOVA table and test the significance of the overall model at 5% level.
- Consider the following data on Y, X1 and X2.
Y: 10 20 40 30 50
X1: 2 5 3 8 7
X2: 1 0 1 2 1
a.) Fit a linear model of Y on X1 and X2. Interpret the regression coefficients.
b.) Calculate R2 and interpret it.
c.) Test at 5% Level H0: R2 = 0 Vs H1: R2 ≠ 0.
- ) Explain the various methods of detecting multicollineartiy.
- Consider the following observed and expected Y values obtained from a linear regression model of Y on X.
Observed Y: 12.4 14.4 14.6 16.0 11.3 10.0 16.2 10.4 13.1 11.3
Expected Y: 12.1 21.4 18.7 21.7 12.5 10.4 20.8 10.2 16.0 12.0
Use spearmen’s rank correlation test to test for the presence of
heteroscedasticity (Assume the level of significance to be 0.05).
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