Programming meeting #8
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The document summarizes the key steps in performing a least squares regression analysis on data to calculate the slope and y-intercept of the linear regression line. It discusses defining arrays to store the x and y coordinate data, functions to calculate summations and the sum of x times y for the data, and the formulas to calculate the slope using these summations and the number of data points. It also covers calculating the y-intercept from the slope and summations. The document concludes by asking for any questions and thanking attendees for the meeting.
![Programming
Meeting #8
DataLeast Squares
Array
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-9-320.jpg)
![Programming
Meeting #8
x
y
O
1
2
3
4
1 2 3 4 65 7
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]
Least Squares
0
2 3
4
Data
1](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-10-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
Summation( )
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]
x 15.0
xΣ](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-16-320.jpg)
![Summation(
Programming
Meeting #8
The slopeLeast Squares
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]
y 12.3)
Σy](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-17-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]
def Summation(array)
sum = 0.0
for e in array
sum = sum + e
end
return sum
end](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-18-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
xyΣ
x = [1.0, 2.0, 3.0, 4.0, 5.0]
y = [1.3, 1.8, 2.8, 2.5, 3.9]
* * * * *
1.3 3.6 8.4 10.0 19.5
42.8](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-22-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
xyΣ while
sum = 0.0
i = 0
i < x.length
sum = sum + x[i] * y[i]
i = i + 1
end
The number
of elements in x](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-24-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
xyΣ while
sum = 0.0
i = 0
i < x.length
sum = sum + x[i] * y[i]
i = i + 1
end
in other languages
for (i = 0; i < x.length; i++) {
sum = sum + x[i] * y[i];
}
keep in
mind…](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-25-320.jpg)
![Programming
Meeting #8
The slopeLeast Squares
xyΣ while
sum = 0.0
i = 0
i < x.length
sum = sum + x[i] * y[i]
i = i + 1
end
def SumXY(x, y)
end
return sum](https://image.slidesharecdn.com/programmingmeeting8-150218182939-conversion-gate02/85/Programming-meeting-8-26-320.jpg)
Programming meeting #8
- 3. Programming Meeting #8 Least Squares x y O 1 2 3 4 1 2 3 4 65 7 Error
- 4. Programming Meeting #8 Least Squares x y 1 2 3 4 1 2 3 4 65 7 y- intercept Slope
- 8. Programming Meeting #8 DataLeast Squares Variable Array Coordinates (X,Y)
- 9. Programming Meeting #8 DataLeast Squares Array x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9]
- 10. Programming Meeting #8 x y O 1 2 3 4 1 2 3 4 65 7 x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9] Least Squares 0 2 3 4 Data 1
- 11. Programming Meeting #8 n xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ The slope The number of points Arrays Least Squares
- 12. Programming Meeting #8 n xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ The slopeLeast Squares ∑xy ∑x ∑y ∑x^2 ∑x Function
- 13. Programming Meeting #8 The slopeLeast Squares xΣ SummationArray Float
- 14. Programming Meeting #8 The slopeLeast Squares xΣ for ine x end sum = 0.0 sum = sum + e
- 15. Programming Meeting #8 The slopeLeast Squares xΣ for ine array end sum = 0.0 sum = sum + e def end return sum Summation ( )array
- 16. Programming Meeting #8 The slopeLeast Squares Summation( ) x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9] x 15.0 xΣ
- 17. Summation( Programming Meeting #8 The slopeLeast Squares x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9] y 12.3) Σy
- 18. Programming Meeting #8 The slopeLeast Squares x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9] def Summation(array) sum = 0.0 for e in array sum = sum + e end return sum end
- 19. Programming Meeting #8 n xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ The slopeLeast Squares Σx2 ∑x ∑y ∑x
- 20. Programming Meeting #8 The slopeLeast Squares Σx2 for ine array end sum = 0.0 sum = sum + e def end return sum Summation2 ( )array **2
- 21. Programming Meeting #8 The slopeLeast Squares xyΣn xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ ∑x ∑y ∑x∑x^2
- 22. Programming Meeting #8 The slopeLeast Squares xyΣ x = [1.0, 2.0, 3.0, 4.0, 5.0] y = [1.3, 1.8, 2.8, 2.5, 3.9] * * * * * 1.3 3.6 8.4 10.0 19.5 42.8
- 23. Programming Meeting #8 The slopeLeast Squares xyΣ for in
- 24. Programming Meeting #8 The slopeLeast Squares xyΣ while sum = 0.0 i = 0 i < x.length sum = sum + x[i] * y[i] i = i + 1 end The number of elements in x
- 25. Programming Meeting #8 The slopeLeast Squares xyΣ while sum = 0.0 i = 0 i < x.length sum = sum + x[i] * y[i] i = i + 1 end in other languages for (i = 0; i < x.length; i++) { sum = sum + x[i] * y[i]; } keep in mind…
- 26. Programming Meeting #8 The slopeLeast Squares xyΣ while sum = 0.0 i = 0 i < x.length sum = sum + x[i] * y[i] i = i + 1 end def SumXY(x, y) end return sum
- 27. n xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ ∑x ∑y ∑x^2 ∑x Programming Meeting #8 The slopeLeast Squares ∑xy
- 28. Programming Meeting #8 The slopeLeast Squares (n*SumXY(x,y) - Summation(x) * Summation(y)) / (n*Summation2(x) - Summation(x)**2) n xy x y n x x2 2 α ( ) = Σ −Σ Σ Σ − Σ ∑xy ∑x ∑y ∑x^2 ∑x
- 29. Programming Meeting #8 Least Squares n x.length y.length or The slope Array.length The number of elements in Array
- 30. Programming Meeting #8 y x n β α = Σ − Σ The slope Least Squares The y-intercept (Summation(y) - a*Summation(x)) / n
- 34. Programming Meeting #8 Thank you for Meeting!