What is the final fitted regression equation for the five-point example data?

Conditions

• The data set consists of the five specific points (1,2), (2,4), (3,5), (4,4), and (5,5).
• The slope $b_1$ has been calculated as 0.6.
• The intercept $b_0$ has been calculated as 2.2.

Reasoning, step by step

1. Identify the computed intercept $b_0 = 2.2$.
2. Identify the computed slope $b_1 = 0.6$.
3. Substitute both coefficients into the general regression form $\hat{y} = b_0 + b_1x$.
4. Write the final equation as $\hat{y} = 2.2 + 0.6x$.

Example

The video displays a summary box listing $b_0=2.2$, $b_1=.6$, and $\hat{y}=2.2+.6x$. The speaker states, "And so y hat is equal to two point two plus point six times x."

Common misconceptions

• Writing the equation as $y = 2.2 + 0.6x$ without the hat notation for the predicted value.
• Swapping the intercept and slope values.
• Assuming the equation applies to any data set rather than just the specific five points shown.

Watch the explanation

Explore next

• How is the intercept $b_0$ calculated once the slope $b_1$ is known?
• How is the slope $b_1$ computed from the two column sums?
• What does the video say comes after computing the regression line?