Teacher Training in Educational Research and Statistical Analysis - Session 6: Beginning Regression Analysis

I used to draw linear regression curves with Python, so it’s nice to see regression analysis covered like this.

I was able to listen to today’s content rather lightly.

1. Historical Background of Regression Analysis

In regression analysis, “regression” means returning to the mean value.

A scientist named Galton analyzed height data for parents and children, drew a straight line using the average values for each interval, and then drew an average line.

The interesting thing is that even if you swap the x-axis and y-axis, the slope of the line comes out similar.

Through this, it was found that the result of regression analysis is not about some genetic secret between parents and children, but rather a mathematical property of regression analysis.

You can see the corresponding paper below.

Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.

2. Correlation Coefficient (Correlation)

This is a statistical index that shows in what direction and how another variable changes when one variable changes.

The value obtained by linear regression represents the degree of correlation between the two variables, not a physical proportional relationship between them.

This is called the correlation coefficient.

3. Reflections

Today’s content was really easy, so I just went through it quickly.

I was going to look up and write down a linear regression function in Python for the first time in a while, but since it’s been some time, I couldn’t recall it well.

import numpy as np

x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])

slope, intercept = np.polyfit(x, y, 1)

print(slope, intercept)

As expected, you really have to study consistently and look at things often.