Year Number of Graduates
(in millions)
2009 15.4
2010 15.9
2011 16.3
2012 16
2013 15.7
a. Code the years using t = 1 for 2009 and fit a quadratic function to the data with
the regression program on your calculator.
equation is ________________________________
b. Predict the # of graduates in 2025. _______________________
To fit a quadratic function to the given data, we can use a regression analysis. Here's how you can do it using a calculator:
a. Code the years using t = 1 for 2009: To code the years, we need to assign a numerical value to each year. Since t = 1 corresponds to the year 2009, we can code the years as follows:
| Year | Code (t) |
|------|----------|
| 2009 | 1 |
| 2010 | 2 |
| 2011 | 3 |
| 2012 | 4 |
| 2013 | 5 |
b. Fit a quadratic function to the data: Using a regression program on your calculator, you can input the coded years and the number of graduates to find the quadratic equation that fits the data. Since the calculator model you're using is not specified, I can provide a general procedure.
1. Enter the coded years (t) in one list and the number of graduates in another list.
2. Access the regression program on your calculator. This is usually found in the stats, graph, or regression menu. Look for a regression program that can fit a quadratic equation to the data.
3. Select the appropriate regression model (e.g., quadratic, quadratic regression, or a similar option) and specify the coded year list as the x-values and the number of graduates list as the y-values.
4. Run the regression analysis and obtain the fitted quadratic equation.
The quadratic equation should be of the form: y = a * t^2 + b * t + c, where a, b, and c are coefficients specific to the data. Once you have the equation from the regression, you can proceed to predicting the number of graduates in 2025.
b. Predict the number of graduates in 2025: Since we have coded the years with t = 1 for 2009, we can calculate the code (t) for the year 2025 as follows:
t = 2025 - 2009 + 1
t = 17
Now we can substitute this value of t into the quadratic equation obtained from the regression analysis to predict the number of graduates in 2025.