Question

find the regression equation, letting the first variable be the predictor (x) variable. using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 400 metric tons of lemon imports. is the prediction worthwhile? use a significance level of 0.05.
lemon imports 225 262 354 485 546
crash fatality rate 16 15.7 15.5 15.4 14.9

find the equation of the regression line.
ŷ = 16.526 + ( - 0.0027 )x
(round the y-intercept to three decimal places as needed. round the slope to four decimal places as needed.)
the best predicted crash fatality rate for a year in which there are 400 metric tons of lemon imports is \\(\square\\) fatalities per 100,000 population.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = 16.526 + (-0.0027)x$, where $x$ is the lemon imports (in metric tons) and $\hat{y}$ is the predicted crash fatality rate.

Step2: Substitute x = 400 into the equation

Substitute $x = 400$ into the regression equation:
$\hat{y} = 16.526 + (-0.0027)(400)$
First, calculate $(-0.0027)(400) = -1.08$
Then, add to the y - intercept: $16.526 - 1.08 = 15.446$

Step3: Round to one decimal place

Round $15.446$ to one decimal place. Looking at the second decimal place (4), which is less than 5, we round down. So $15.446\approx15.4$

Answer:

15.4