statistics

Regression Terminology

x y (y-yavg) 2 (x-xavg)*(y-yavg) x

2 y

2 x*y ŷ = b + ax error error 2

2 3 3.06 7.00 4.00 9.00 6 2.90 0.10 0.01 6 4 0.56 0.00 36.00 16.00 24 4.75 -0.75 0.56 7 6 1.56 1.25 49.00 36.00 42 5.21 0.79 0.62 9 6 1.56 3.75 81.00 36.00 54 6.13 -0.13 0.02

column total 24 19 6.75 12.00 170.00 97.00 126 19.00 0.00 1.21 column avg (sum/n) 6.00 4.75 1.69 3.00 column stdev (sample) 2.94 1.50 0.78

column stdev (pop) 2.55 1.30 variance (pop) 6.50 1.69 n 4

covariance 3.00

r = covariance/( σ x * σ y ) 0.91

r 2

0.82

0.46

1.98

covariance

Column 1 Column 2

Column 1 6.5 Column 2 3.00 1.69

correlation

Column 1 Column 2

Column 1 1

Column 2 0.91 1

r 2

0.82

𝒃 = 𝒏 𝒙𝒚 − 𝒙 𝒚

𝒏 𝒙𝟐 − 𝒙 𝟐

𝒂 = 𝒚 − 𝒃𝒙

y = 0.4615x + 1.9808 R² = 0.8205

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10

y

x

y vs. x

𝑺𝒕𝒅 𝑬𝒓𝒓𝒐𝒓 𝒐𝒇 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 = 𝒆𝒓𝒓𝒐𝒓𝟐

𝒏−𝟐 =