Unraveling Linear Models: Solving n*Sum(XiYi) - Sum(XiYi)

In summary, the conversation revolves around linear models and verifying a calculation involving the sum of products of x and y values. The discussion also includes finding the values of Betas and simplifying the equation. The conclusion is that the sum of products can be simplified to sum(xy) - n<x><y>.
  • #1
retspool
36
0
Linear models is the topic

And i believe my professor wrote this n*Sum(XiYi) - Sum(XiYi) = Sum(Xi - Xbar)(Yi - Ybar)

i was hoping if some one could tell me if this is true of if it is my bad in typing down.

If it is true then can some one please tell me how?

I've attached an image i'd appreciate it if someone could explain to me the last 3 steps.

Thanks
 

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  • #2
And this too. I've written simplifies at the center of the paper, i don't know how they get the Betas.


Thanks
 

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  • #3
Let <x> and <y> denote the x and y averages (you called them Xbar Nd Ybar). You want S = sum{(xj -<x>)(yj - < y>): j=1...n}. The nth term, expanded out, is xj*yj - <x>*yj - <y>*xj + <x>*<y>. Now sum <x>*yj = <x>*sum yj = n*<x>*<y>, etc., so we end up with S = sum(xy) - 2*n*<x>*<y> + n*<x>*<y> = sum(xy) - n<x><y>.

RGV
 

Related to Unraveling Linear Models: Solving n*Sum(XiYi) - Sum(XiYi)

1. What are linear models?

Linear models are statistical models that assume a linear relationship between the dependent variable and one or more independent variables. This means that the relationship between the variables can be represented by a straight line on a graph.

2. What is the equation for a linear model?

The equation for a linear model is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

3. What is the purpose of "Unraveling Linear Models: Solving n*Sum(XiYi) - Sum(XiYi)"?

This formula is used to calculate the slope of a linear regression line, which is a type of linear model. It is used to determine the relationship between two variables and make predictions about future data.

4. How do you solve for the slope using this formula?

To solve for the slope, you will need to first calculate the sum of the products of the x and y values (n*Sum(XiYi)) and the sum of the x values multiplied by the sum of the y values (Sum(Xi)*Sum(Y)). Then, subtract the latter from the former and divide by the sum of the squared x values (Sum(Xi^2)) minus the sum of the x values squared (Sum(Xi)^2).

5. Can this formula be used for non-linear models?

No, this formula is specifically for linear models. Non-linear models have different equations and require different methods for solving.

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