One estimates Y     X   X   X   with 65 observations and gets RSS  315.4 . He wants to test
the specification of his regression with Ramsey’s RESET. Therefore he estimates the following regression
equation: Y     X   X   X   Yˆ   Yˆ   Yˆ X   with corresponding observations and gets
RSS  265.2 . Execute the test and get the conclusion at 2% significance level.
0
1
1
2
2
3
3
2
0
1
1
2
2
3
3
4
3
5
4
6
6
There are two models to be compared with the same dependent variable and observations belonging to it. First
model has 5 regressors and the second model has 6. Both models are estimated with 124 observations and the
RSS for the models are 1723.5 and 1655.8. Use Akaike’s Information Criterion to decide the model to be
preferred.
Solve the last question with Scwartz Criterion.
One is estimating the demand for a commodity, say Y with its own price X OP , its substitutes price, X SP , and the
complements price X CP . So that the regression model used is: Y     (OP)   (SP)   (CP)   .
a. What are the expected signs of the partial regression coefficients?
0
OLS estimation results are Y  
0
OP
SP
CP
 12.4 (OP )  5.2 ( SP)  2.1 (CP)
b. Is there anything unusual with these results? What is the possible source of the mistake?
c. What can you say about the correlation between the (possible) omitted variable and the included varaibles?
(Hint: Use the bias formula)
You estimate the regression equation of your model but find some of the regressors that determine the dependent
variable insignificant. You realize that there is an irrelevant variable included in the regression. What can you
say about the correlation between the insignificant variable and the irrelevant one?
One estimates Y   0  1 X 1   2 X 2   3 X 3   with 32 observations and gets RSS  127.1 . He
wants to test the specification of his regression with Ramsey’s RESET. Therefore he estimates the
following regression equation: Y   0  1 X 1   2 X 2   3 X 3   4Yˆ 2   5Yˆ 3   6Yˆ 4   with
corresponding observations and gets RSS  119.3 . How can he conclude about the specification of the
regression equation at 5% significance level.
There are two models to be compared. First model has 4 regressors and the second model has 7. Both
models are estimated with 53 observations and the RSS for the models are 1723.5 and 955.8. Use AIC
and SC Critera to decide the model to be preferred.
One estimates the PRF of Y     X   X   but forgets to include X which is relevant.
The partial regression coefficient of X is positive . How does this omission affect the coefficient
estimate of X 1 if the correlation between X 1 and X is negative?
0
1
1
2
2
3
3
3
An irrelevant variable is included when estimating a PRF. What would be the effect of this on the
confidence intervals of the partial regression coefficients?
You calculate the Akaike’s Information Criterion to compare two models, say Model 1 and Model 2. The AIC
you have for the first model is 22.5 whereas it is 27 for Model 2. Which of these models should be selected?
An irrelevant variable is included when estimating a PRF. What would be the effect of this on the
significance tests of the partial regression coefficients?
We would like to compare 3 models with 32 observations and the same dependent variable. Model 1 has 4
regressors and ESS1=18.3, Model 2 has 6 regressors and ESS2=29.1, and Model 3 has 7 regressors and
ESS3=9.23. Which of these 3 models should be selected according to Akaike’s Information Criterion if
TSS=38.2?
[20 points] One estimates Y     X   X   X   with 25 observations and return RSS=55.2. He
has some doubts about the specification of the model and decides to use Ramsey’s RESET in order to test for the
misspecification of the model. Therefore he estimates the augmented regression of
Y     X   X   X   Yˆ   Yˆ   Yˆ   and calculates RSS=36.5. Test for the specification of
the original model at α=1%.
0
1
1
2
2
0
1
1
2
2
3
3
2
3
3
4
3
4
5
6
The correct specification of a PRF is Y     X   . One mistakenly adds the irrelevant variable X 2 and
misspecifies the model as: Y     X   X   . He estimates the misspecified model with 32
observations. Test for the significance of 1 both in correctly specified and misspecified models at α=5% if
  48.3 ,  x12  30.3 and the correlation between X 1 and X 2 is -0.88. Explain how the inclusion of the
irrelevant variable affects the significance test of 1 with the help of your findings.
0
1
0
1
1
1
2
2
2
One estimates Y     X   X   with 26 observations and returns ESS=1256.87. He has some doubts
about the specification of the model and decides to use Ramsey’s RESET in order to test for the
misspecification of the model. Therefore he estimates the augmented regression of
Y     X   X   Yˆ   Yˆ   Yˆ   and calculates the ESS of the augmented regression as
ESS=1785.91. Test for the specification of the original model at α=1% if the TSS=2184.22.
0
1
1
2
2
2
0
1
1
2
2
3
3
4
4
5
Explain why Ramsey’s RESET can detect misspecification of omitted variables and functional forms but not
irrelevant variables.
There are 3 models with 42 observations and the same dependent variable to be compared. Model 1 has 4
regressors and RSS1=158.33, Model 2 has 6 regressors and RSS2=268.21, and Model 3 has 7 regressors and
RSS3=93.23. Which of these 3 models should be selected according to Akaike’s Information Criterion?
Two models, estimated with 30 observations, are to be compared. Comparison with AIC prefers Model 1 but
comparison with SC prefers Model 2. What are the conditions on k and RSS for these models to make this
possible?
AIC and SIC calculated for the same model return the same values. Under which conditions is this possible?
One estimates the PRF of Y     X   X   but forgets to include X which is relevant, ie X is the
omitted variable here. The partial regression coefficient of X is positive,   0 . How does this omission
affect 1 , if the correlation between X 1 and X is negative?
0
1
1
2
2
3
3
3
3
3
There are two models to be compared. First model has 4 regressors and the second model has 7. Both
models are estimated with 53 observations and the RSS for the models are 1723.5 and 955.8. Use AIC
and SC Critera to decide the model to be preferred.
Assume that the correct population model is the following:
y  0  1 x1  2 x2  u . We assume that this model
satisfies the classical assumptions. When we estimate this model, we get OLS estimators which are unbiased.
Explain what happens to OLS estimator of  when we
1
a. include an irrelevant variable and estimate y  
b. omit x and estimate y  
2
0
 1 x1  
0
 1 x1  2 x2  3 x3  
.