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The line of best fit for a data set is \(y = 1.1x + 3.4\). Find the residual for each of the coordinate pairs, \((x,y)\).
Plots of the residuals for four different models of the same data set are displayed. Which of the following represents the plot of the residuals from a model that fits its data best?
A residuals plot. Horizontal from 0 to 10, by 1's. Vertical, negative 4 to 4, by 0 point 5's. 10 dots as follows: 1 comma 3 point 46, 2 comma 2 point 22, 3 comma negative 0 point 03, 4 comma 2 point 73, 5 comma 0 point 49, 6 comma negative 0 point 25, 7 comma negative 2 point 2, 8 comma negative 1 point 94, 9 comma negative 1 point 48, 10 comma negative 1 point 22.
A residuals plot. Horizontal from 0 to 10, by 1's. Vertical, negative 4 to 4, by 0 point 5's. 10 dots as follows: 1 comma 0 point 74, 2 comma 0 point 06, 3 comma negative 1 point 61, 4 comma 1 point 7, 5 comma 0 point 03, 6 comma negative 0 point 15, 7 comma negative 1 point 52, 8 comma negative 0 point 7, 9 comma 0 point 32, 10 comma 1 point 14.
A residuals plot. Horizontal from 0 to 10, by 1's. Vertical, negative 4 to 4, by 0 point 5's. 10 dots as follows: 1 comma negative 1 point 5, 2 comma negative 2, 3 comma negative 3 point 5, 4 comma 0, 5 comma negative 1 point 5, 6 comma negative 1 point 5, 7 comma negative 2 point 7, 8 comma negative 1 point 7, 9 comma negative 0 point 5, 10 comma 0 point 5.
A residuals plot. Horizontal from 0 to 10, by 1's. Vertical, negative 4 to 4, by 0 point 5's. 10 dots as follows: 1 comma 3 point 32, 2 comma 2 point 64, 3 comma 0 point 96, 4 comma 4 point 28, 5 comma 2 point 61, 6 comma 2 point 43, 7 comma 1 point 05, 8 comma 1 point 87, 9 comma 2 point 89, 10 comma 3 point 71.
A local car salesperson created a scatter plot to display the relationship between a car’s 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.
A scatterplot. Horizontal, from 0 to 12, by 1’s, age of car, years. Vertical, from 0 to 35000, by 5000’s, car sale price, dollars. 12 dots, trend linearly downward and right, dot 1 at 1 comma 20000 and dot 12 at 12 comma 2500 with line of best fit.
The car salesperson looks at the residuals for the car sales.