Summation Simplification for Neumerator of Beta Estimator

In summary, the equation Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi can be simplified to Ʃi w_i(x_i-\sum_j x_j w_j/\sum_k w_k) y_i, where the term in brackets is x minus <x> and each summation has a separate index. This is a clearer representation of the equation and will make it easier to solve. Thank you for the assistance.
  • #1
LBJking123
13
0
I need simplify this equation:

Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

Into an equation of the form: Ʃ(something - something)yi

I am pretty sure the first something is xiwi, but I have no idea what the second something would be...

Any help would be greatly appreciated. Thanks!
 
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  • #2
LBJking123 said:
I need simplify this equation:

Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

Into an equation of the form: Ʃ(something - something)yi

I am pretty sure the first something is xiwi, but I have no idea what the second something would be...

Any help would be greatly appreciated. Thanks!

Come on, that's easy:
[itex]
\sum_i w_i(x_i-\sum_j x_j w_j/\sum_k w_k) y_i
[/itex]
Note that I chose a separate index for each summation for clarity.
The term in brakets is x minus <x>, i.e. the mean of x.
 
  • #3
Ohhhhh I kept thinking it was going to be

Ʃ(xiwi-(xiwi2)/Ʃwi)yi

I makes more sense when you choose a separate index for each summation.

Thanks for the help DrDu!
 

Related to Summation Simplification for Neumerator of Beta Estimator

1. What is the purpose of Summation Simplification for the Neumerator of Beta Estimator?

The purpose of Summation Simplification for the Neumerator of Beta Estimator is to simplify the calculation process for the numerator of the Beta Estimator formula. This makes it easier and more efficient for researchers to estimate a population parameter using a sample.

2. How does Summation Simplification work for the Neumerator of Beta Estimator?

Summation Simplification involves rearranging the terms in the numerator of the Beta Estimator formula to reduce the number of summations needed for the calculation. This is achieved by grouping similar terms together and using algebraic manipulations to simplify the expression.

3. What are the benefits of using Summation Simplification for the Neumerator of Beta Estimator?

The main benefit of Summation Simplification is that it reduces the computational burden of calculating the Beta Estimator. This can save time and resources, particularly when working with large datasets. It also makes the estimation process more accurate by minimizing the potential for errors in the calculation.

4. Are there any limitations to Summation Simplification for the Neumerator of Beta Estimator?

While Summation Simplification can greatly improve the efficiency of the Beta Estimator calculation, it may not always be possible to simplify the expression. This is because the level of simplification depends on the specific values and variables in the equation. In some cases, the expression may not be able to be simplified at all.

5. How can I determine if Summation Simplification is appropriate for my research?

If you are using the Beta Estimator in your research, it is worth exploring whether Summation Simplification is possible for your specific equation. This can be done by examining the expression and determining if there are any opportunities for grouping or simplifying terms. You can also consult with a statistician or conduct further research to see if others have applied Summation Simplification to similar equations in the past.

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