ecotrix

[Seecha]

5.1.State with reason whether the following statements are true, false, or uncertain.
Be precise.
a... The t test of significance discussed in this chapter requires that the
sampling distributions of estimators ˆ β1 and ˆ β2 follow the normal
distribution.
b... Even though the disturbance term in the CLRM is not normally distributed,
the OLS estimators are still unbiased.
c... If there is no intercept in the regression model, the estimated ui (= ˆui )
will not sum to zero.
d... The p value and the size of a test statistic mean the same thing.
e... In a regression model that contains the intercept, the sum of the residuals
is always zero.
f... If a null hypothesis is not rejected, it is true.
g... The higher the value of σ 2, the larger is the variance of ˆ β2
h... The conditional and unconditional means of a random variable are the
same things.
i... In the two-variable PRF, if the slope coefficient β2 is zero, the intercept
β1 is estimated by the sample mean ¯Y.
j... The conditional variance, var (Yi | Xi ) = σ 2, and the unconditional variance
of Y, var (Y) = σ 2
Y , will be the same if X had no influence on Y
.
.
.
my answers are
a. true
b.true
c.false
d.doubtful
e.false , as it alwys sums up to zero
f.false , depends on alpha , in how no. out of 100.
g. true
h. false
i. true
j. false . as var. is only affected by ui
.
.
.
help me out where i m wrong ?

[Seecha]

Let ρ2 represent the true population coefficient of correlation. Suppose
you want to test the hypothesis that ρ2 = 0. Verbally explain how you
would test this hypothesis??
.
.
.
this one too.

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d. p value provide the smallest level of significance at which the null hypothesis would be rejected, it can't exceed 1, where test statistic (like t-statistic and f-statistic) can exceeds 1.

j. Y^ = a + bX + u
  because slope coefficient is 0.

 Y^ = a +u

in deviation form
y^ = u - E(u)

which doesn't depend on X
E((y^)^2) also doesn't depend on X

So, both conditional and unconditional variance will be same

[happy]

R^2 = 0 means the no explanatory variable is able to explain the variation in the Explanatory variable, which is same as testing for the multiple linear restriction that is all the slope coefficient are 0, under the alternative hypothesis that at least 1 slope coefficient is non 0.

So we can use the F-test to check the increase in R^2 from the restricted model (in which R^2 = 0 because all slope coefficient are 0) to the unrestricted model is statistically significant or not.

[Seecha]

thank you .. :) :)
if i do all chaptrs till  dummy variable regression .. is this enough fr dse entrance  

[happy]

i recommend


2-6 chapter from Econometrics by Example (or same topics from any book)
 
model mis-specification specification error till over fitting and under fitting included appendix of those from Basic Econometrics by gujrati

Appendix C except GLS from Basic Econometrics (matrix notation of regression model)

and some basic concept (like unbiased, consistent property)

Both book PDF available on internet