Question

8. Prediction error = Y – Y’, this means that the prediction error is negative when the predicted value of Y is larger than the observed value of Y. Explain the logic of why one subtracts Y’ from Y in computing the prediction error.

Answer 1

after fitting regression model we test on data, and compair actual data and predicted data.

y=actual value

y^ =is oredicted value

suppose we take y-y^

y=10 , y^ =5

=10-5= 5

but in case

y=10 and y^ = 15

=10-15= -5

but we dont messure error in negateve value,,like time distence.

in this case we avoide this problem taking absolute value or take square

| y= y^ | absolute error

(y-y^) ^2 square of error

in regression problem we use mostly square of error,it can be very easy to calculate, easy to understand , very aappropriate as copmaire to absolute value,

why square:1) ignore minus sign

2)and give punishment of error , means your error is 4 then we punish to 16,if your error is 10 then they punish to you 100,

thats why we messur small error also,,

thanks hope you are understand