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 525 metric tons of lemon imports. is the prediction worthwhile? use a significance level of 0.05.
lemon imports: 228, 267, 358, 491, 542
crash fatality rate: 16.1, 16, 15.6, 15.6, 15.1
find the equation of the regression line.
\hat{y} = 16.693 + (-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 525 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 $\hat{y} = 16.693 + (-0.0027)x$, where $x$ is the lemon imports (in metric tons) and $\hat{y}$ is the predicted crash fatality rate.

Step2: Substitute x = 525 into the equation

Substitute $x = 525$ into the regression equation:
$\hat{y} = 16.693 + (-0.0027)(525)$

Step3: Calculate the value

First, calculate $(-0.0027)(525) = -1.4175$
Then, add to the y-intercept: $16.693 - 1.4175 = 15.2755$

Step4: Round to one decimal place

Round $15.2755$ to one decimal place, which is $15.3$.

Answer:

15.3