How are the y-deviations $y - \bar{y}$ calculated from the table?

Conditions

• The y-values in the table are 2, 4, 5, 4, and 5.
• The sample mean $\bar{y}$ has been computed as 4.

Reasoning, step by step

1. Identify the mean of the y-values, $\bar{y}=4$.
2. Subtract 4 from the first y-value: $2 - 4 = -2$.
3. Subtract 4 from the second y-value: $4 - 4 = 0$.
4. Subtract 4 from the third y-value: $5 - 4 = 1$.
5. Subtract 4 from the fourth y-value: $4 - 4 = 0$.
6. Subtract 4 from the fifth y-value: $5 - 4 = 1$.

Example

The video computes 2 minus 4, 4 minus 4, 5 minus 4, and so on, filling the $y - \bar{y}$ column with -2, 0, 1, 0, and 1. Dashed vertical segments connect points to the horizontal mean line at $y=4$.

Common misconceptions

• Adding the mean to the y-values instead of subtracting it.
• Calculating absolute distances instead of signed deviations.
• Assuming the deviations are calculated from the regression line rather than the mean line.

Watch the explanation

Explore next

• What does the column ($x - \bar{x}$)($y - \bar{y}$) represent in the regression table?
• How is the slope $b_1$ computed from the two column sums?
• Why must the regression line pass through the point (3,4) in the example?