Answer
(a) A linear model is more or less appropriate for these data, as the scatter plot approximately fits a straight line.
(b) $y=-0.000105x+14.5$. Also see the blue line graph on the image.
(c) $y=-0.0001x+13.95$. See the red line on the graph.
(d) $y=-0.0001\times25000+13.95=11.45$
Rate for $25000$ Dollars income will be $11.45$ per 100 population.
(e) $y=-0.0001\times80000+13.95=5.95$
Rate for $80000$ Dollars income will be $5.95$ per 100 population.
(f) $y=-0.0001*200000+13.95=-6.05$ (NOT appropriate)
Work Step by Step
(a) A linear model is more or less appropriate for these data, as the scatter plot approximately fits a straight line.
(b) Using the formula $y-y_(1)=m(x-x_{1})$ we can find an equation for this graph:
$(8.2-14.1)=m(60000-4000)$
$m=\frac{-5.9}{56000}\approx -0.000105$
Now we can input values to find $b$ ($y$-intercept):
$8.2=-0.000105(60000)+b$
$b=14.5$
So, we get a linear equation:
$y=-0.000105x+14.5$
(c) Using a special calculator (or this could even be done approximately by hand), the regression line is calculated to be:
$y=-0.0001x+13.95$
(d) Income is considered as $x$ value, so we will just input 25000 Dollars into the equation:
$y=-0.0001\times25000+13.95=11.45$
Rate for $25000$ Dollars income will be $11.45$ per 100 population.
(e) We will do the same as in the previous case; input 80000 Dollars:
$y=-0.0001\times80000+13.95=5.95$
Rate for $80000$ Dollars income will be $5.95$ per 100 population.
(f) In case of 200000 Dollars income, we will have:
$y=-0.0001*200000+13.95=-6.05$ (Note, amount of people can't be negative)
So, in this case the linear model will be inappropriate.
