1) For each of the four countries, based on the graph, what kind of function will best model the data? Explain your reasoning.
Data is from www.gapminder.org
Data is from www.gapminder.org
2) Type the following three regression models into Desmos. Which function best fits the data? How do you know?
\(y_1\sim mx_1+b\) \(y_1\sim ax_1^2+bx_1+c\) \(y_1\sim ab^{x_1}\)
3) In Desmos, click on the data folder from 1968-2017. This shows the data from the past \(50\) years along with linear, quadratic and exponential regression models. Which set of data, the data from 1800-2017 or the data from 1968-2017 is the best predictor of incomes in the US in 2030?
4) In Desmos, click on the data folder for 2018-2040. These are projected incomes in the US for the future. Do any of the models (linear, quadratic, exponential) predict the data points that you see in Desmos? Explain.
5) Why might the equations of best fit not match up with the predicted data points?
6) Open up the folder with the data from 1800-2017. Delete both the x and y column for the years 1931, 1932, 1933, 1934 and 1935. Delete any other years from the table that you think are outliers. How does the adjustment change the equations of best fit?
7) Decide whether to include or exclude outliers. Decide whether to look at data since 1800 or only for the last \(50\) years. Write the equation that is the best fit of the data. Explain your equation.
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