# Partial Slope Coefficients - Introduction to Econometrics - Exam, Exams for Econometrics. Alagappa University

## Econometrics

Description: Partial Slope Coefficients, Econometric Study, Steps Involved in Conduct, Coefficient of Multiple Determination, Confidence Interval, Regression Relationship, Consequences for OLS are points from questions of the Introduction to Econometrics exam.
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Ollscoil na hÉireann, Gaillimh GX_____
National University of Ireland, Galway
Examinations 2010/2011
Exam Code(s) 3BA1, 3BA5, 3BA6, 4BA4, 4BA8, 1EM1, 1OA1, 3BC1,
4BC2, 4BC3, 4BC4, 4BC5, 1EK3, 1EK2, 1EK3, 3FM1
Exam(s) B.A., B.A. (ESS), B.A. (PSP), B.A. (Int’l), Erasmus,
Occasional, B.Comm., B.Comm. (Language),
H.Dip.Econ.Sc. 3rd B.Sc.(Fin. Maths & Economics)
Module Code(s) EC422
Module(s) Applied Econometrics
Paper No.
Repeat Paper 1
External Examiner(s) Dr Pat McGregor
Internal Examiner(s) Professor John McHale
Professor Ciaran O’Neill
Duration 2 hours
No. of Pages
Department(s) Economics
Course Co-ordinator(s) Ciaran O’Neill
Requirements:
Statistical Tables
Graph Paper
EC422 Applied Econometrics Resit 2011
All questions carry equal marks.
Students answer four questions in 2 hours
1.
a. Briefly detail the steps involved in the conduct of an econometric study (8
marks)
b. Outline the principles underlying ordinary least squares regression
analysis (9 marks)
c. Distinguish between the coefficient of multiple determination and the
adjusted coefficient of multiple determination. Which would use when
assessing a regression function and why? (8 marks)
2a. Give an account of the desirable properties of an estimator (7 marks)
b. Construct the 95% confidence intervals for the predicted value of Y in the
following regression function when X = 262.5 and when X = 345. (10
marks)
^
Y = 7.6182 + 0.0814X1i
_^
Where n = 10, X = 262.5, σ2= 6.4864 and Σxi2= 51562
c. Interpret and comment on the confidence interval (8 marks)
3
You are given the following data based on 15 observations:
___
Y = 0.2033; X1= 1.2873; X2= 8.0; Σyi2= 0.016353
Σx1i2= 0.359609; Σx2i2= 280; Σx1iyi= 0.066196
Σx2iyi= 1.60400; Σx1ix2i = 9.82000
(Note, lower case letters denote deviations about the mean)
a. Estimate the intercept and partial slope coefficients (12 marks)
b. Test the statistical significance of each slope coefficient using α= 0.05 (8
marks)
c. Comment on the regression relationship (5 marks)
4a. What is multi-collinearity and what are its consequences for OLS
estimators (12 marks)
b. Detail how you ascertain whether a model suffered from multi-collinearity
(7 marks)
c. With use of examples briefly detail common sources of multi-collinearity
(6marks)
5a. Briefly discuss what is meant by “under” and “over” estimation in
regression analysis and outline the impact of each on OLS estimates (12
marks)
b. Detail the steps involved in the conduct of the WALD test (6 marks)
c. What, if any, impact will errors in measurement with respect to the
dependent or independent variable have on OLS estimators. (7 marks)
6a. What is heteroscedasticity and what are its consequences for OLS
estimators (8 marks)
b. Outline the method of weighted least squares as a means of addressing
heteroscedasticity (8 marks)
c. What is meant by autocorrelation, and how would you test for it? (9
marks)
Formulae Sheet EC422 Econometrics
Two variable model
^_^_
β0= Y – β1X
^
β1=Σxiyi
Σxi2
_ _
xi= (Xi– X) and lower case y = (Yi– Y)
^ ^
Variance of β0= Var(β0) = (ΣXi2/ n Σxi2) . σ2(note this involves upper and lower case
“x”
^ ^ ^
Standard error β0= SE (β0) = Var(β0)
^ ^
Variance of β1= Var(β1) = σ2/Σxi2{as before lower case “x” is used to denote
deviations}
^ ^ ^
Standard error β1= SE (β1) = Var(β1)
^
σ2is estimated by σ2= (Σei2) / n-2
^
Σei2=Σ(Yi– Yi)2
r2= 1 - Σei2/Σyi2
^
Σyi2=β1Σxi2+Σei2
Jarque-Berra test
JB = n/6 [S2+ (K – 3)2/4]
Where S is skewness and K kurtosis
Forecasting
Mean = E(YX0) = β0+β1X0
_
Var = σ2[1/n + (X0– X)2/Σxi2]
^
Where σ2is the variance of Ui(unknown) approximated by σ2
Confidence interval on forecast
^ ^ ^
β0+β1X0+ or - tα/2 SE(Y0)