APPC 2.6 Competing Function Model Validation

The graphs give three residual plots for linear, quadratic, and exponential regressions. Which of the following is true about the residual plots for these regressions?

• The residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. Therefore, the quadratic model is appropriate.

• The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the linear and exponential models are appropriate.

• The residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. Therefore, the linear and exponential models are appropriate.

• The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the quadratic model is appropriate.

• The error is 0.01, and the value predicted by the model is an underestimate.

• The error is 0.01, and the value predicted by the model is an overestimate.

• The error is 0.03, and the value predicted by the model is an underestimate.

• The error is 0.03, and the value predicted by the model is an overestimate.

The speed of a car traveling on a highway is recorded once per second for two minutes. During this time interval, the car gradually speeds up slightly to pass another vehicle, then returns to its original speed. The recorded speed with respect to time can be modeled by linear, quadratic, and exponential functions. For each of the three models, their residuals are small and are without pattern. Which of the following conclusions is best?

• A linear model is best based on contextual clues.

• A quadratic model is best based on contextual clues.

• An exponential model is best based on contextual clues.

• Contextual clues fail to help in selecting a model for this contextual situation.

Students in a science class are constructing a model for a data set. The residual plot for their quadratic regression model is given. Which of the following is the best conclusion?

• The quadratic model is appropriate because the residuals show a pattern.

• The quadratic model is appropriate because the residuals show no pattern.

• The quadratic model is not appropriate because the residuals show a pattern.

• The quadratic model is not appropriate because the residuals show no pattern.

Use the table showing the number of alternative-fuel vehicles (thousands) in the United States for selected years from 1996 to 2010. A function A(t) is used to model the data, in thousands, for 6 ≤ t ≤ 20, where t = 6 corresponds to 1996. Which of the following could be a plot of the residuals of the model?

• A

• B

• C

• D