Use the following data to answer 7a, 7b, and 7c..... {(1, 3), (2, 2.2), (3, 3), (5, 7), (8, 5)}

Question

{(1, 3), (2, 2.2), (3, 3), (5, 7), (8, 5)}

7a) Find a cubic and a quadratic model for the table of values.

7b) Which model appears to give the better fit?

7c) Using the model you selected in part b, estimate the value of y when x = 12.

Answer 1

7a.) {(1, 3), (2, 2.2), (3, 3), (5, 7), (8, 5)} Use the Regression Calculator to input points and it will generate a regression model automatically. You will need the regression model and make sure to look at R² to see if it is the best fit.

Cubic Regression Model: y = 6.6156 - 5.2288x + 1.7805x² - 0.144x³ with R² = 0.9993

Quadratic Regression Model: y = 0.3678 + 1.682x - 0.1319x² with R² = 0.5969

7b.) The cubic regression model gives a better fit because of the coefficient of determination. This determines how well a regression model fits the data. Its values are between 0 and 1 (similar to correlation). Since the cubic regression model has a R² closer to 1, it tells us that it represents the data accurately.

7c.) y = 6.6156 - 5.2288(12) + 1.7805(12)² - 0.144(12)³ = 6.6156 - 62.7456 + 256.392 - 248.832 = - 48.57