Question

What does a residual value of –4.5 mean in reference to the line of best fit?

Answer 1

The residual value is the difference between the observed value (from the scatter plot) and the predicted value (from the line of best fit).

Explanation:

The residual value is the difference between the observed value (from the scatter plot) and the predicted value (from the line of best fit).

Residual Value = Observed Value - Predicted Value

Since the residual value of -4.5 is negative, we can say the predicted value is larger than the observed value. In other words, the line of best fit is "above" the scatter plot point in that specific point.

Answer 2

The actual or observed data point is below the line of best fit.

Explanation:

Since we know that residual is the difference between the observed value of the dependent variable (y) and the predicted value (ŷ) of a regression model. Residual tells us that how far the data falls from the regression line.

`\text{Residual}=\text{Observed value- Predicted value}`

• If we have a positive value for residual, this means dependent variable's actual value is greater than its predicted value.

• If we have a negative value for residual, this means dependent variable's actual value is less than its predicted value.
• For data points above the line, the residual is positive, and for data points below the line, the residual is negative.

`-4.5=\text{Observed value- Predicted value}`

`\text{ Predicted value}-4.5=\text{Observed value}`

Since our given residual value is -4.5, therefore, observed or actual value of dependent variable is 4.5 less than its predicted value and it is below line of best fit.