Question

4 a local car salesperson created a scatter plot to display the relationship between a cars sale price in dollars, y, and the age of the car in years, x. the scatter plot and the line of best fit are displayed in the graph. the car salesperson looks at the residuals for the car sales. a. for a car that is 4 years old, does the salesperson sell above or below her expected selling price? explain your reasoning. b. for a car that is 12 years old, does the salesperson sell above or below her expected selling price? explain your reasoning.

Explanation:

Step1: Understand residual concept

Residual = Observed value - Predicted value. If residual > 0, observed value (actual sale price) > predicted value (value on line of best fit). If residual < 0, observed value < predicted value.

Step2: Analyze 4 - year - old car

On the scatter - plot, for \(x = 4\) (age of car), the data point (observed value) is above the line of best fit (predicted value). So, residual=Observed - Predicted>0.

Step3: Analyze 12 - year - old car

On the scatter - plot, for \(x = 12\) (age of car), the data point (observed value) is on the line of best fit (predicted value). So, residual = Observed - Predicted = 0.

Answer:

a. Above. Because the data point for a 4 - year - old car is above the line of best fit.
b. On (neither above nor below). Because the data point for a 12 - year - old car is on the line of best fit.