Part A:
A scatter plot is a set of points plotted on a horizontal and vertical axes. If we use the left column as the 'horizontal' variable and the right column as the 'vertical' variable, we have the following scatterplot:
Part B:
Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line. A line equation has the form:
[tex]y=mx+b[/tex]
where m represents the slope and b the y-intercept.
Using the least square method to determinate those coefficients, the line regression model equation for our dataset is:
[tex]y=-24.14x+161.2[/tex]
For this line we have the following graph:
Exponential regression models use an exponential curve. A exponential equation has the form:
[tex]y=a(b)^x[/tex]
Where a represents the initial value and b represents the growth/decay rate.
Using the exponential regression model, we have the following equation:
[tex]y=178.7015\cdot0.7643^x[/tex]
This equation has the following graph:
Part C:
The slope/multiplier represents the rate the graph decreases. On the context of the problem, the rate that new cases appear.
Part D:
For each model, we just have to solve the following equation:
[tex]y=100[/tex]
Solving for the linear model, we have:
[tex]\begin{gathered} 100=-24.14x+161.2 \\ \implies x=\frac{100-161.2}{-24.14}=2.53521127... \end{gathered}[/tex]
Solving for the exponential model, we have:
[tex]\begin{gathered} 100=178.7015\times0.7643^x \\ \implies x=\frac{\ln100-\ln178.7015}{\ln0.7643}=2.15981269... \end{gathered}[/tex]
