2. [40 points] Given the US population data set PopulationData.csv [4], determine a linear regression solution...

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2. [40 points] Given the US population data set "PopulationData.csv" [4], determine a linear regression solution for the data. The data is for the US (total) population from 1950 to 2017 shifted to start in 1950 (that is, "year 0" is the year 1950). Do this by doing the following: a. [5 points] Plot the data (scatter plot) using some plotting software or online tool. b. [10] Set up and solve (again, using software) the normal equations for the linear regression (least square) function. c. [5] Give the equation of the resulting line and plot it with the given data. 3. [40 points] From calculus, we learned that the basic population growth model (where we assume the rate of growth is proportional to the population size) is given by P(t) = Poekt, where P is the initial (1950) population and k is the growth constant (this model is sometimes called the Malthusian model). Determine an exponential regression model by doing the following: a. [5] Generate the y-data as the natural log (In(y)) of the given population data (y). b. [10] Generate the linear regression solution for this new data set. (Note that the slope of the line is the growth constant for the exponential model. What does the y intercept of the line represent?) c. [5] Plot the (raw) data and the exponential solution on the same graph. What is the value of k for your model? 4. [10 points] For each of these models (linear and exponential) project the population to the year 2100. Compare the results. Which, if either, do you feel is more accurate. Explain. 2. [40 points] Given the US population data set "PopulationData.csv" [4], determine a linear regression solution for the data. The data is for the US (total) population from 1950 to 2017 shifted to start in 1950 (that is, "year 0" is the year 1950). Do this by doing the following: a. [5 points] Plot the data (scatter plot) using some plotting software or online tool. b. [10] Set up and solve (again, using software) the normal equations for the linear regression (least square) function. c. [5] Give the equation of the resulting line and plot it with the given data. 3. [40 points] From calculus, we learned that the basic population growth model (where we assume the rate of growth is proportional to the population size) is given by P(t) = Poekt, where P is the initial (1950) population and k is the growth constant (this model is sometimes called the Malthusian model). Determine an exponential regression model by doing the following: a. [5] Generate the y-data as the natural log (In(y)) of the given population data (y). b. [10] Generate the linear regression solution for this new data set. (Note that the slope of the line is the growth constant for the exponential model. What does the y intercept of the line represent?) c. [5] Plot the (raw) data and the exponential solution on the same graph. What is the value of k for your model? 4. [10 points] For each of these models (linear and exponential) project the population to the year 2100. Compare the results. Which, if either, do you feel is more accurate. Explain.