Why must the regression line pass through the point (3,4) in the example?

Conditions

• The data set has a computed mean for x, $\bar{x}=3$.
• The data set has a computed mean for y, $\bar{y}=4$.
• The context is simple linear regression.

Reasoning, step by step

1. Compute the mean of the x-values to find $\bar{x}=3$.
2. Compute the mean of the y-values to find $\bar{y}=4$.
3. Locate the intersection point $(\bar{x}, \bar{y}) = (3,4)$ on the scatter plot.
4. Apply the stated property that the regression line must pass through this mean point.

Example

The narrator says, "It turns out that all regression lines have to go through that point there. That's where the mean of the independent variable and the mean of the dependent variable cross." The point is labeled (3,4) on the graph.

Common misconceptions

• Assuming the regression line passes through the origin (0,0).
• Believing the line must pass through the median of the data points.
• Thinking that the line passes through (3,4) only because the data happens to be symmetric.

Watch the explanation

Explore next

• Why can we substitute $x=3$ and $y=4$ to find the intercept?
• How is b0 calculated once b1 is known?
• What is the final regression equation for the example data?