Introduction:

This post is focused on basic concepts in linear regression and I will share how to calculate baseline prediction, SSE, SST, R2 and RMSE for a single variable linear regression.

Dataset:

The following figure shows three data points and the best-fit regression line: y = 3x + 2.

The x-coordinate, or “x”, is our independent variable and the y-coordinate, or “y”, is our dependent variable.

Baseline Prediction:

Baseline prediction is just the average of values of dependent variables. So in this case:

(2 + 2 + 8) / 3 = 4

It won’t take into account the independent variables and just predict the same outcome. We’ll see in a minute why baseline prediction is important.

Here’s what the baseline model would look like:

SSE:

SSE stands for Sum of Squared errors.

Error is the difference between actual and predicted values.

So SSE in this case:

= (2 – 2)^2 + (2 – 5)^2 + (8 – 5)^2

= 0 + 9 + 9

= 18

SST:

SST stands for Total Sum of Squares.

Step 1 is to take the difference between Actual values and Baseline values of the dependent variables.

Step 2 is to Square them each and add them up.

So in this case:

= (2 – 4)^2 + (2 – 4)^2 + (8 – 4)^2

= 24

R2:

Now R2 is 1 – (SSE/SST)

So in this case:

= 1 – (18/24)

= 0.25

RMSE:

RMSE is Root mean squared error. It can be computed using:

Square Root of (SSE/N) where N is the # of dependent variables.

So in this case, it’s:

SQRT (18/3) = 2.44