Hi so I am trying to figure out how the unexplained variatio

Hi, so I am trying to figure out how the unexplained variation formula can equal it\'s alternate formula. An example of this follows:

I am trying to figure out the proof. I have written the formulas down below:

we might need to incorporate the following formulas in the proof as well:

Please show the steps of the proof, thank you very much!

Hi, so I am trying to figure out how the unexplained variation formula can equal it\'s alternate formula. An example of this follows: sum_{i=1}^{n}(y_i - hat{y_i})^2 = sum_{i=1}^{n}(y_i)^2- b_0 sum_{i=1}^{n}y_i-b_1 sum_{i=1}^{n}x_iy_i I am trying to figure out the proof. I have written the formulas down below: Unexplained variation = sum_{i=1}^{n}(y_i - (yhat)_i)^2 Unexpained variation (alternate form) = sum_{i=1}^{n}y_i^2- b_0 sum_{i=1}^{n}y_i-b_1 sum_{i=1}^{n}x_iy_i we might need to incorporate the following formulas in the proof as well: b_0= bar{y}-b_1 bar{x} .............. b_1=(-b_0+ bar{y})/bar{x} ...........................................b1= (sum_{i=1}^{n}(x_i-bar{x})y_i)/(sum_{i=1}^{n}(x_i-bar{x})^2

Solution

if yes extend the time.