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
...
is the prediction worthwhile?
a. since there appears to be an outlier, the prediction is not appropriate.
b. since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile.
c. since common sense suggests there should not be much of a relationship between the two variables, the prediction does not make much sense.
d. since the sample size is small, the prediction is not appropriate.

Explanation:

To determine if the prediction is worthwhile, we analyze the relationship between lemon imports (a measure of a fruit's import volume) and crash fatality rates (a measure of traffic safety). Logically, there should be no inherent or causal relationship between these two variables (lemon imports don't directly affect crash fatality rates). Option A is incorrect as there's no obvious outlier. Option B is incorrect because the requirements for a meaningful regression (like a logical relationship between variables) aren't met here. Option D is incorrect as sample size alone doesn't determine worthiness if the relationship is illogical. Option C correctly points out that common sense suggests no meaningful relationship, so the prediction doesn't make sense.

Answer:

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