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Consider a k-variables linear regression model, i.e., Y = X 1β1 + X 2 β2 + ε, Where, X1 is (N k1 ) , X 2 is (N k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional regressors (β2 ) is larger than one.
A measure of value of money in an economy is what?
the desire to hold money in liquid form instead of investing it is what?
Problem 1
Consider a k-variables linear regression model, i.e.,
Y = X 1β1 + X 2 β2 + ε,
Where, X1 is (N k1 ) , X 2 is (N k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional
regressors (β2 ) is larger than one.
Problem 3
In this question we look at the relation between the logarithm of weakly earnings and years of education. Using data from the national longitudinal study of youth, we find the following results for a regression of log weekly earnings and years of education, experience, experience squared and an intercept:
Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2
( 0.222) ( 0.008) ( 0.025) (0.001)
c). Labour economist studying the relation between education and earnings are often concerned about what they call “ability bias”. Suppose that individuals differ in ability, and that the correct specification of the regression function is one that includes ability:
log ( earnings )I = β1 + β 2 ⋅ educI + β 3 ⋅ experI − β 4 ⋅ experI2 + β5 ⋅ abilityI + εI .
In this regression, what do you expect the sign of β5 (the coefficient on ability) to be?
Problem 2
Let X1 , X2 , ⋯, XN be a random sample of size n from normal distribution with mean μ and variance σ2 .
a). Find the maximum likelihood estimator of σ2 2 . (2 points)
b). Find the asymptotic distribution of the maximum likelihood estimator of σ2 2
obtained in part (a).
Problem 1
Consider a k-variables linear regression model, i.e.,
Y = X 1β1 + X 2 β2 + ε,
Where, X1 is (N k1 ) , X 2 is (N k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional
regressors (β2 ) is larger than one.
Problem 3
A random sample Y1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density
function is given by: f (Y ) = βe− βY , Y 0 & β > 0
a). Obtain the maximum likelihood estimator (MLE) of β.
b). Given that Σ n
Y i = 25 ,
Σn
Yi2
= 50 , n = 50 calculate the maximum likelihood
i =1
i =1
estimate of β.
(3 point)
c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative
hypothesis that β ≠1at 5% level of significance.
7. Explain following concepts by using appropriate graphs.
1. Price elasticity of demand
2. Income elasticity of demand
3. Cross price elasticity of demand
4. Market equilibrium
5. Government interference in the market
A. The tomatoes that RADA has purchased will be distributed to outlets in other parishes. Could we assume that there is a national shortage of tomato? State your opinion on the
matter.
Quantity Supplied (000 lb.)
MARKET
SUPPLY
(000 lb.)
PRICE OF
TOMATO
$
MARKET
DEMAND
(000 lb.)
FARMER
Q
FARMER
R
FARMER
Y
30
500
50
25
25
40
400
100
60
40
50
300
130
100
70
60
200
185
125
90
70
100
220
180
100
