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
(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 15.3 fatalities per 100,000 population.
(round to one decimal place as needed.)
is the prediction worthwhile?
a. since the sample size is small, the prediction is not appropriate.
b. since common sense suggests there should not be much of a relationship between the two variables, the prediction does not make much sense.
c. since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile.
d. since there appears to be an outlier, the prediction is not appropriate.

Explanation:

To determine if the prediction is worthwhile, we analyze the relationship between lemon imports (predictor) and crash fatality rates. Common sense tells us there should be no logical connection between lemon imports and crash fatality rates (e.g., lemon imports don't directly influence traffic safety). So the prediction doesn't make sense. Option A is incorrect as sample size alone isn't the main issue here. Option C is wrong because the relationship lacks logical basis. Option D is incorrect as there's no obvious outlier affecting the relationship's logic.

Answer:

B. Since common sense suggests there should not be much of a relationship between the two variables, the prediction does not make much sense.