Q$2$A: The table below gives the poverty level, unemployment rate, high school graduation rate, and divorce rate $($all in percentages$)$ of $10$ randomly selected states in $2007.$ Find the correlation between each of the variables and poverty level.

Determine a linear combination of predictor variables to predict poverty level. How good is your model. Based on this data, does divorce rate appear to be an influencer?

$\backslash$table$[[\backslash$table$[[$Poverty$],[$Level$]],\backslash$table$[[$Unemployment$],[$Rate$]],\backslash$table$[[$High School$],[$Graduation Rate$]],\backslash$table$[[$Divorce$],[$Rate$]]],[14\mathrm{.}3,4\mathrm{.}3,69\mathrm{.}6,3\mathrm{.}9],[9\mathrm{.}3,3\mathrm{.}8,71\mathrm{.}9,3\mathrm{.}7],[8\mathrm{.}9,3\mathrm{.}8,86\mathrm{.}5,2\mathrm{.}6],[12\mathrm{.}8,5\mathrm{.}3,81\mathrm{.}9,3\mathrm{.}8],[5\mathrm{.}8,3\mathrm{.}5,81\mathrm{.}7,3\mathrm{.}8],[15\mathrm{.}5,5,68\mathrm{.}6,4],[12\mathrm{.}8,5\mathrm{.}3,73\mathrm{.}8,3\mathrm{.}9],[9\mathrm{.}4,2\mathrm{.}7,82\mathrm{.}5,3\mathrm{.}1],[10,4,88\mathrm{.}6,3\mathrm{.}6],[11,4\mathrm{.}5,88\mathrm{.}5,2\mathrm{.}9]]$

$1$

Q$2$B$-$ The following table gives the number of deer in a hypothetical forest for various years between $1941$ and $1982.$ Our goal is to model the population in terms of the year.

TABLE $3\mathrm{.}4$

$\backslash$table$[[$Year$,1941,1947,1951,1957,1962,1965,1971,1977,1982],[$Population$,12,500,28,500,7,000,20,000,6,500,12,000,4,000,11,000,3,500]]$

To make the data values smaller and easier to work with, we transform them by subtracting $1941$ from the year and dividing the population by $1000,$ yielding the data in Table $3\mathrm{.}5.$

Plot the data and fit the following equation using least square error to determine the coefficients. Superimpose a plot of the model on data points.

$y=a+bx+$ccos$(\frac{x}{5})+$dsin$(\frac{x}{5}).$