Medical Statistics (full English class). Ji-Qian Fang School of Public Health Sun Yat-Sen University. Chapter 12 Linear Correlation and Linear Regression. 12.3 Linear regression. Initial meaning of “regression”: Galdon noted that if father is tall, his son
School of Public Health
Sun Yat-Sen University
Initial meaning of “regression”:
Galdon noted that if father is tall, his son
will be relatively tall; if father is short, his
son will be relative short.
Given the value of chest circumference (X), the vital capacity (Y) vary around a center (y|x)
Try to estimate and , getting
a -- estimate of , intercept
b -- estimate of , slop
-- estimate of y|x
To find suitable a and b such that
Standard deviation of regression coefficient
Standard deviation of residual
Sum of squared residuals
1) To describe how the value of Y depending on X
2) To estimate or predict the value of Y through a value of X (known)
-- based on the regression of Y on X.
3) To control the value of X through a value of Y (known)
-- If X is not a random variable,
based on the regression of Y on X.
-- If X is also a random variable,
based on the regression of X on Y.
1. Distinguish and connection
Correlation: Both X and Y are random
Regression: Y is random
X is notrandom – Type regression
X is alsorandom – Type regression
1) Same sign for correlation coefficient
and regression coefficient
2) t tests are equivalent
tr = tb
, the sum of squared residuals is
for regression and correlation
-- sometimes may be indirect relation or even no any real relation;
A big value of rdoes not necessary mean a big regression coefficient b;
4) To reject H0: ρ=0 does not necessary mean the correlation is strong -- ρ≠0;
5) Scatter diagram is useful before working with linear correlation and linear regression;
6) The regression equation is not allowed to be applied beyond the range of the data set.