Reference no: EM131132265
1. A linear regression model is given below:
Yi = β1 + β2Xi + ui i = 1, 2, ... N
Where the assumption of the classical linear regression model hold. Instead of the OLS estimator, the researcher decided to use the following estimator
Β^2 = Y3-Y2/X3-X2
Where Y2 and Y3 are the second and third observation of the Y's and X2 and X3 are the second and third observation of X's.
a. Show that β^2 is a linear estimator.
b. Prove that β^2 is an unbiased estimator of the true regression slop parameter, β2.
c. Derive the variance of β^2. (i.e., express the variance of β^2 in terms of X's and σ2, where σ2 = Var(ui)).
2. The linear regression model is given below:
yi = β0 + β1xi + ui i = 1, 2, .... n
Let β^0 and β^1 be the OLS intercept and slope coefficient estimator, respectively, and let u- be the sample average of the errors (not the residuals!).
a. Show that β^0 can be written as β^0 = β0 + u- - (β^1 - β1)x-.
b. Show that Var(β^0) = σ2/n + σ2(x-)2/SSTx-.
c. Show that Var(β^0) = (σ2n-1i-1∑nxi2/i-1∑n(xi - x-)2).
3. The Linear regression model is given below:
Yi = β1 + β2Xi + ui i = 1, 2, ... n
The following information is derived from a sample of observations:
∑Yi = 1110, ∑Xi = 1680, ∑Yi2 = 133,300, ∑Xi2 = 315,400 and ∑XiYi - 204,200
a. Calculate β^1 and β^2.
b. Calculate SST, SSE, SSR and R2.
c. Calculate the value for σ^2, var(β^1) and var(β^2).
The eruption of brutal warfare in europe
: How and why does she see the eruption of brutal warfare in Europe in 1914 as but an extension into Europe of European imperialism previously practiced on other peoples in other parts of the globe?
|
Describe some of characteristics of well-designed storyboard
: Describe some of the characteristics of a well-designed storyboard. Predict the impact that a poorly developed storyboard could have on a Website.
|
An opportunity to mentor on entrepreneurship youths
: You are give an opportunity to mentor on entrepreneurship youths in developing countries ,- what are the challenges you are likely to be faced by most of the youths you will be mentoring?
|
Are these methods applicable to the united states
: Do you think China's experience in raising its standard of living (output per person) provides a model for developing countries to follow?
|
Calculate sst sse and ssr
: The following information is derived from a sample of observations: ∑Yi = 1110, ∑Xi = 1680, ∑Yi2 = 133,300, ∑Xi2 = 315,400 and ∑XiYi - 204,200, Calculate SST, SSE, SSR and R2
|
How many quarters has each recession lasted
: In terms of length and magnitude, which two recessions have been the most severe?
|
What does rosa luxemburg see
: What does Rosa Luxemburg see as the likely outcome of a German victory in the World War on the one hand, or an Anglo-French victory on the other to her?
|
Review rosa luxemburgs analysis of the first world war
: Review Rosa Luxemburg's analysis of the First World War in here 1916 "The War and the Workers." What according to Luxemburg were the consequences of European Social Democrats' failure to block their nations' governments going to war in 1914?
|
How the southern slaver-holder class succeed
: How the southern slaver-holder class succeed in forcing the free states of theNorth to accept slavery over ever-greater parts of the U.S. and its territoriesbefore 1860.
|