Q: The error term is homoskedastic if a. var (εi | Xi = x) is constant...
Q: The error term is homoskedastic if
a. var (εi | Xi = x) is constant for i = 1,…, n.
b. var (εi | Xi = x) depends on x
c. Xi is normally distributed
d. there are no outliers
d. the value of Yi is changes in a constant way
Homework Answers
Option a.
It refers to a condition where in the variance of the residual term in regression model is constant. So with homoskedasticity, the regression model would be accurate as the error term would not get influenced by the variables.
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Q: The error term is homoskedastic if
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Log-lin model in simple regression: yi=B0.B1Xi.eui take natural log of both sides lnyi=lnB0 + (lnB1)xi +...
Log-lin model in simple regression:
yi=B0.B1Xi.eui
take natural log of both sides
lnyi=lnB0 + (lnB1)xi +
ui . Take lnyi = wi,
lnB0= B*0 and
lnB1=B*1 so the former equation
equals to wi= B*0 +
B*1 + ui. It is said that, when
you increase x by 1 unit, you expect B*1 %
change in y.
B*1
=(dyi/yi) / dxi =
= (((yi-yi-1)/yi) /
(xi- xi-1))*100 . question is about the
numerator, (yi-yi-1)/yi)*100:
1)It is said that the numerator reflects...
Let Yi = Xiß + d E(eiXi) = 0. You observe (X,, Yi) with XXri where ri is a random error. Derive t...
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4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance Var(X)-σί. Let Żi-(X,-μ.)/oi so that Zi , . . . , Ζ,, are independent and each has a N(0, 1) distribution. Show that LZhas a x2 distribution. Hint: Use the fact that each Z has a xî distribution i naS
7. Show that σ2 E(X-0 and Var(X if X1, . . . , Xn are independent and identically distributed with E(Xi) = 0 and E(X2) = σ2 for i = 1,-.. , n
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Log-lin model in simple regression:
yi=B0.B1Xi.eui
take natural log of both sides
lnyi=lnB0 + (lnB1)xi +
ui . Take lnyi = wi,
lnB0= B*0 and
lnB1=B*1 so the former equation
equals to wi= B*0 +
B*1 + ui. It is said that, when
you increase x by 1 unit, you expect B*1 %
change in y.
B*1
=(dyi/yi) / dxi =
= (((yi-yi-1)/yi) /
(xi- xi-1))*100 . question is about the
numerator, (yi-yi-1)/yi)*100:
1)It is said that the numerator reflects...
Let Yi = Xiß + d E(eiXi) = 0. You observe (X,, Yi) with XXri where ri is a random error. Derive the probability limit of the OLS estimator in the regression of Yi on X,. For simplicity, assume that EX Er0 Your probability limit should have the form β(1-stuff), where stuff depends only on the population variances of ri and X¡. The correct result will highlight that if stuff < 1 then the probability limit of the OLS estimator...
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