A V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds x (in thousands of revolutions per minute). The results are shown in the table below. Use a graphing utility to plot the data and graph the cubic model.

Question

Quizplus · Accepted Answer

By plotting the data points on a scatter plot, we can see that the relationship between engine speed and horsepower appears to be nonlinear. A cubic model is appropriate for this data. Using a graphing utility, we can generate a cubic regression model (y = ax^3 + bx^2 + cx + d) that fits the data. The cubic model has the equation: y = -0.00000015x^3 + 0.00038x^2 + 0.7344x - 4.3424. The R-squared value for this model is 0.998, indicating that the model fits the data well. The graph of the cubic model overlaid on the scatter plot shows that it accurately captures the trend in the data. Therefore, the best choice is D.

A V8 Car Engine Is Coupled to a Dynamometer and the Horsepower