Question

what does a residual value of -4.5 mean in reference to the line of best fit? the data point is 4.5 units above the line of best fit. the data point is 4.5 units below the line of best fit. the line of best fit is not appropriate to the data. the line of best fit has a slope of -4.5.

Explanation:

A residual is calculated as the actual value of a data point minus the predicted value from the line of best fit (\( \text{Residual} = y - \hat{y} \), where \( y \) is the actual value and \( \hat{y} \) is the predicted value). A negative residual means the actual value (\( y \)) is less than the predicted value (\( \hat{y} \)), so the data point is below the line of best fit. A residual of -4.5 means \( y - \hat{y} = -4.5 \), or \( y = \hat{y} - 4.5 \), so the data point is 4.5 units below the line. The other options are incorrect: a positive residual would be above the line, residuals don't indicate if the line is inappropriate, and residuals are unrelated to the slope of the line.

Answer:

B. The data point is 4.5 units below the line of best fit.