In this lesson, we will demonstrate the difference between Errors Functions like: - Standard Error SE. - Mean Absolute Error MAE. - Mean Square Error MSE. - Weighted Mean Square Error WMSE. - Root Mean Square Error RMSE. LinkedIn: https://www.linkedin.com/in/hassan-badawy/

1. Hassan Badawy
Ai
Simplification
Series
5- Errors Functions

2. Hassan Badawy
Y
X
100
200
300
400
500
k
50
100
50
150
200
50
300
250
𝑚2
100
150
200
150
250
200
Solution Model2 Linear Regression
Area Price
(k)
100 200
150 400
200 450
250 550
300 450
x y ො𝑦
ො𝑦
e2
e1
e3
e4
e5
𝐞 = ෝ𝒚 - y
𝑒1+𝑒2+𝑒3+𝑒4+𝑒5
5
y = m x + b
y = w0 + w1 x ---> (1)
Error
Parametric solution
ො𝑦
y

3. Hassan Badawy
Linear RegressionSolution Model2 Error Functions
Standard Error
𝒆𝒊 = ො𝑦𝒊 − 𝒚𝒊
𝐸 = 𝑒1 + 𝑒2 + 𝑒3
𝑬 = σ𝒊 𝒆𝒊 = σ𝒊=𝟏
𝒏
(ො𝑦𝒊 − 𝒚𝒊)
Y
300
𝑚2
250
X
100
200
300
400
500
k
50
100
150
200
+50
-100
+75
𝐸 = +50 − 100 + 75 = 25

4. Hassan Badawy
Linear RegressionSolution Model2 Error Functions
Mean Absolut Error MAE
MA𝐸 =
𝑒1 + 𝑒2 + 𝑒3
3
𝑴𝑨𝑬 =
𝟏
𝒏
σ𝒊=𝟏
𝒏
𝒆𝒊 =
𝟏
𝒏
σ𝒊=𝟏
𝒏
ෝ𝒚 − 𝒚
MA𝐸 =
+50 + −100 + +75
3
MA𝐸 =
50+100+75
3
= 75
Y
300
𝑚2
250
X
100
200
300
400
500
k
50
100
150
200
+50
-100
+75

5. Hassan Badawy
𝑀𝑆𝐸 =
(𝑒1)2+(𝑒2)2+(𝑒3)2
3
𝑴𝑺𝑬 =
𝟏
𝟐𝒏
σ𝒊=𝟏
𝒏
𝒆𝒊
𝟐
=
𝟏
𝒏
σ𝒊=𝟏
𝒏
(ො𝑦𝒊 − 𝒚𝒊) 𝟐
Linear RegressionSolution Model2 Error Functions
Mean Square Error MSE
Y
300
𝑚2
250
X
100
200
300
400
500
k
50
100
150
200
+50
-100
+75
𝑀𝑆𝐸 =
(+50)2+(−100)2+(+75)2
3
𝑀𝑆𝐸 =
2500+10000+5625
3
= 6041.67
W𝑀𝑆𝐸 =
𝑀𝑆𝐸
𝑤
=
𝑀𝑆𝐸
2
= 320.83

6. Hassan Badawy
Linear RegressionSolution Model2 Error Functions
Root Mean Square Error RMSE
𝑅𝑀𝑆𝐸 =
(𝑒1)2+(𝑒2)2+(𝑒3)2
3
R𝑴𝑺𝑬 =
𝟏
𝒏
σ𝒊=𝟏
𝒏
𝒆𝒊
𝟐 =
𝟏
𝒏
σ𝒊=𝟏
𝒏
(ො𝑦𝒊 − 𝒚𝒊) 𝟐
Y
300
𝑚2
250
X
100
200
300
400
500
k
50
100
150
200
+50
-100
+75
𝑅𝑀𝑆𝐸 = 𝑀𝑆𝐸 = 6041.67 = 77.73

7. Hassan Badawy
SE MAE MSE WMSE RMSE
25 75 6041 3020 78
෍
𝒊
𝒆𝒊
𝟏
𝒏
෍
𝒊=𝟏
𝒏
𝒆𝒊
𝟏
𝟐𝒏
෍
𝒊=𝟏
𝒏
𝒆𝒊
𝟐
𝟏
𝒏
෍
𝒊=𝟏
𝒏
𝒆𝒊
𝟐 𝟏
𝒏
෍
𝒊=𝟏
𝒏
𝒆𝒊
𝟐
Linear RegressionSolution Model2 Error Functions

8. Hassan Badawy
Ai
Simplification
Series