Standard Error of Regression: Graphical Representation

• The standard error of the regression (SER) is a measure of the accuracy of predictions made by a regression model.

• It represents the average distance that the observed values fall from the regression line.

• The formula for the standard error of the regression is:

• N is the number of observations

Graphical Representation

• To illustrate the concept of the standard error of regression, let’s consider a simple linear regression example.

• Suppose we have a dataset with a linear relationship between the independent variable X and the dependent variable Y.

The graph will show:

1. The scatter plot of the observed data points.

2. The regression line.

3. The residuals (vertical lines from observed points to the regression line).

Pharmaceutical Example

Scenario

Let's consider a pharmaceutical study where researchers are investigating the relationship between the dosage of a drug (in mg) and the response of patients (measured as reduction in symptoms on a standardized scale).

Data

Here's a sample dataset:

Let's fit a linear regression model to this data, plot the graph, and calculate the standard error of the regression.

Explanation

• Observed data points: blue dots

• Regression line: Red line

• Residuals: Blue dotted lines from each data point to the regression line

Data

Here's the dataset used in the study:

Standard Error of Regression

• The standard error of regression for this model is approximately 1.05. This indicates the typical distance between the observed symptom reduction values and the regression line, providing a measure of the model's accuracy.

This analysis helps researchers understand how well the dosage of the drug predicts the reduction in symptoms, with the standard error giving an idea of the typical prediction error size.