Chapter 5 Prediction and Standard Error AWS

Chapter 5 Correlation and Regression

Prediction and Standard Error

Correlation and prediction % Fat

Skinfolds

Equation for a line 𝑌 = bX + c

Correlation and prediction % Fat

Skinfolds

Correlation and prediction % Fat Prediction Errors

Skinfolds

Standard Error of Estimate (SEE)

S e  Sy * 1  r Se = SEE = SEP is the STANDARD DEVIATION of the errors of predicting Y from X.

2

Correlation and prediction % Fat

Skinfolds

Correlation and prediction

% Fat 20

23 17

SEE = 3%

Skinfolds

40

The Predicted 𝑌

𝑌= bX + c 𝑌 = .25 * Skinfolds + 10 𝑌 = .25 * 40 + 10 𝑌 = 10 + 10 𝑌 = 20

% Fat 20

23 17

SEE = 3% Skinfolds

40

𝑠𝑦.𝑥 = 𝑠𝑌 1 − 𝑟 2

The Standard Error

Sy = 7 rxy = .90 𝒔𝒚.𝒙 = 𝟕 ∗

𝟏 − . 𝟗𝟎𝟐 % Fat 20

𝒔𝒚.𝒙 = 𝟕 ∗

𝟏 − . 𝟖𝟏

𝒔𝒚.𝒙 = 𝟕 ∗

. 𝟏𝟗

23 17

SEE = 3% Skinfolds

𝒔𝒚.𝒙 = 𝟕 ∗ . 𝟒𝟑

𝒔𝒚.𝒙 = 𝟑

40

Correlation and prediction

% Fat 20

Examples….

26

23 17 14

SEE = 3%

Skinfolds

40

Correlation and prediction X  X z  score  S 26  20 6 z  score    2.0 3 3

Correlation and prediction

% Fat 20

Examples….

23 17 14

SEE = 3% Skinfolds

50.00 – 47.5 = 2.5%

26

40