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–WCC Math 130 Fall 2019 Mrs. Kirsch

MATHEMATICAL MODEL PROJECT

The purpose of this project is to investigate how real world data can be modeled by functions. Sometimes relationships have strong positive or negative linear relationships and therefore a function that relates the two variables can be useful. However, relationships between variables are not always strong and they are not always linear. Your individual project will be shared with your class mates, so make sure it is neat and clear.

PART A : LINEAR MODEL due November 5, 2019

1. Identify two variables that you think may be related. Examples: x = years since 2000,

y = Yankees payroll in year x after 2000; x = amount of Yankee payroll in a certain year, y = amount of Red Sox payroll in the same year; x = year after 2000, y = population of a state (or country, or town);

x = day of year (1 – 365) y = amount of daylight in minutes (subtract sunrise time from sunset time and convert to minutes)

2. Collect 6 – 10 pairs of these variables. YOU MUST GIVE A SOURCE FOR YOUR DATA.

3. Make a scatterplot, either by hand or using a spreadsheet program. Make sure the axes are clearly labeled. You need two copies of the scatterplot.

4. Answer these two questions about your data:

a. Identify the independent variable and the dependent variable, make sure units are clear

b. Does there seem to be a correlation? (Is there a pattern relating the two variables?

If there is a correlation, describe it as best you can.

5. Use the graphing calculator to find and write a linear regression model for your data.

6. Draw the graph of your linear model by hand on one of the scatterplots for your data.

7. Describe how well your linear model matches your data.

8. Use your linear model to make a prediction using interpolation.

9. Use your linear model to make a prediction using extrapolation.