0
How do you use a variance-covariance matrix to obtain least squares estimates?
Wiki User
∙ 13y ago
Suppose that you have simple two variable model:
Y=b0+b1X1+e
The least squares estimator for the slope coefficient, b1 can be obtained with
b1=cov(X1,Y)/var(X1)
the intercept term can be calculated from the means of X1 and Y
b0=mean(Y)-b1*mean(X1)
In a larger model, Y=b0+b1X1+b2X2+e
the estimator for b1 can be found with
b1=(cov(X1,Y)var(X2)-cov(X2,Y)cov(X1,X2))/(var(X1)var(X2)-cov(X1,X2)2)
to find b2, simply swap the X1 and X2 terms in the above to get
b2=(cov(X2,Y)var(X1)-cov(X1,Y)cov(X1,X2))/(var(X1)var(X2)-cov(X1,X2)2)
Find the intercept with
b0=mean(Y)-b1*mean(X1)-b2*mean(X2)
Beyond two regressors, it just gets ugly.
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
Obtain a transformation which will diagonalize the matrix?
consider a matrix Aobtain a transformation which will diagonalize the matrix.Whatare the coordinates of an arbitrary vectora=traspos(x,y,z)with respect to the basis set which diagonalizes A?
What multiplication fact can be found by using arrays for 2 times 9 and 5 times 9?
Assume two matrices are to be multiplied (the generalization to any number is discussed below). Arithmetic process of multiplying numbers (solid lines) in row i in matrix A and column j in matrix B, then adding the terms (dashed lines) to obtain entry ij in the final matrix.If A is an n × m matrix and B is an m × p matrix, the matrix product ABwhere each i, j entry is given by multiplying the entries Aik (across row i of A) by the entries Bkj (down column j of B), for k = 1, 2, ..., m, and summing the results over k:Thus the product AB is defined only if the number of columns in A is equal to the number of rows in B, in this case m. Each entry may be computed one at a time.Refer to link below for more details.
How do you obtain a secondary credit number?
how do i obtain a secondary credit number
What is the difference between obtain and acquire?
There is no substantial difference betweem "obtain" and "acquir."
What is the difference between the graphical and numerical methods of finding the solution of an equation?
The graphical method is often approximate but can be applied to any function. If done on a computer, the region surrounding the solution can be enlarged to obtain more accurate estimates. A numerical method will give an exact result is an analytical solution is possible. If not, the solution will depend on the numerical method used and, sometimes, the starting "guesstimate".
How can one obtain auto repair estimates?
The best way to obtain these estimates would be to go to an auto place and talk with them about it. Shop around, though, to make sure to get the best deal.
When do scientists have to rely on estimate?
Scientists must rely on estimates when they cannot obtain exact numbers.
Obtain a transformation which will diagonalize the matrix?
consider a matrix Aobtain a transformation which will diagonalize the matrix.Whatare the coordinates of an arbitrary vectora=traspos(x,y,z)with respect to the basis set which diagonalizes A?
What math skill do scientist rely on when they cannot obtain exact numbers?
Scientists must sometimes rely on estimates when they cannot obtain exact numbers :)
Where can one obtain car insurance estimates in the United States?
Most car insurance websites will provide car insurance estimates online now. These can be obtained from sites such as Geico, Allstate and Progressive.
Why is extracellular matrix made from pig bladder?
Availability and the pig bladder has the extracellular matrix, so it can regenerate itself. There are hundreds of thousands of pigs, slaughtered every year for food. The bladders are not considered food, so they are thrown away. Which makes them readily available and cheap to obtain. Your liver is an organ that has the matrix and can regenerate itself, but operations are expensive and the donor might not survive the operation.
What is the formula for solving single factor ANOVA?
There is no single formula.It is necessary to calculate the total sum of squares and the regression sum of squares. These are used to calculate the residual sum of squares. The next step is to use the appropriate degrees of freedom to calculate the mean regression sum of squares and the mean residual sum of squares.The ratio of these two is distributed as Fisher's F statistics with the degrees of freedom which were used to obtain the average sums of squares. The ratio is compared with published values of the F-statistic since there is no simple analytical form for the integral.
How far is it from Jacksonville Beach Florida to Biloxi Mississippi?
Total Travel Estimates: 7 hours 27 minutes / 486.97 miles using MapQuest to obtain this information
Where can I obtain decking building plans?
To get decking plans the best thing you can do is call a contractor that gives free estimates. The would usually give you some plans so you can use those.
Why do scientists give estimates?
Scientists give estimates because we are not sure of anything that is out of reach from us that is I mean Space. We are also not sure of the exact distances or the calculation because none has felt it... There are numerous factors that affects the experiments if we consider all the factors and try to obtain the result, we would yield the result after about 500 years. So, Scientists give estimates which mostly are about 89 percent correct according to the recent polls..
What is the average number of people that need CPR a year?
From the information in the related link, from the American Heart Association, these numbers are difficult to obtain. From what I have read, the closest estimates are several hundred thousand in the US.
How much does wired driveway alarm retail for?
The basic way to learn about the cost of a wired driveway alarm would be to start with simply looking on the internet. From there you could obtain a list of local companies and arrange for estimates.
