Teacher Training in Educational Research and Statistical Analysis - Session 7 Simple Regression Model: Intercept and Slope

Today's research question is a bit unusual.

What is the relationship between ice cream sales and the number of drowning accidents?

Let’s assume we have the following hypothetical data.

The regression line drawn for this data is shown below.

What do the slope and intercept mean here?

1. Good regression line vs. bad regression line

How should we estimate the graph in regression analysis?

Of course, by eye we can intuitively say which graph explains the data better, but if you are preparing a paper, you must be able to express this mathematically.

At this point we use something called the residual.

Residual = Actual value - Predicted value.

The smaller the residuals, the better the regression line.

However, simply adding up the residuals causes a problem.

This is because residuals can be positive or negative.

So we calculate something called the sum of squared errors (SSE).

With this, we can analyze how well the regression line fits the data.

2. Linear regression analysis

This is a way of summarizing the relationship between variables with a straight line.

Finding the regression line is the process of finding the intercept and slope.

In linear regression analysis as well, we find the intercept and slope that minimize the sum of squared errors.

3. Reflections

The very idea that we evaluate a regression line using something called the sum of squared errors felt really fresh.

Unlike my previous simple thought that “if the regression line looks similar to the data, then it’s good,” it felt new to realize that we need to define this mathematically and understand that definition.

And the definition itself was not difficult.

I’m leaving today having learned one more thing.