I NEED HELP!!

The table shows the annual consumption of cheese people in the United States foor selected years in the nineteenth century. What cubic model best fits this data?

Year Pounds Consumption
1915 4.156
1922 4.857
1946 7.16
1991 29.989

take a look at using Newton's Divided Differences at

http://www.math.ucla.edu/~ronmiech/YAN/ndivdiff.html

I'd probably offset the year values by 1915 to make the values smaller.

I still do not understand

Im doing this problem also and a I cant figure it out

To determine the cubic model that best fits this data, we can follow these steps:

1. First, let's plot the data points on a graph to visualize the trend. On the x-axis, we'll represent the years, and on the y-axis, we'll represent the pounds of consumption.

2. Now, we need to find the equation of the cubic model that best fits the data. A cubic model has the form: y = ax^3 + bx^2 + cx + d, where a, b, c, and d are coefficients that need to be determined.

3. To find the coefficients, we will use a technique called least squares regression. This involves minimizing the sum of the squares of the differences between the observed data points and the predicted values from the model.

4. We will use a statistical software or a graphing calculator to perform the regression analysis. By inputting the data points into the software or calculator, it will generate the cubic model equation and the corresponding coefficients.

5. Once we have the equation of the cubic model, we can evaluate its goodness of fit by calculating the coefficient of determination (R^2). This value ranges between 0 and 1 and represents the proportion of the variation in the dependent variable (pounds of consumption) that can be explained by the independent variable (years).

6. If the coefficient of determination is close to 1 (e.g., R^2 > 0.9), it indicates a good fit. However, if it's closer to 0 (e.g., R^2 < 0.5), it suggests a poor fit.

By following these steps, you can determine the cubic model that best fits the given data on the annual consumption of cheese in the United States in the nineteenth century.