Step 1 :The first step is to calculate the linear correlation coefficient, also known as Pearson's correlation coefficient. This coefficient measures the strength and direction of the linear relationship between two variables. The formula for calculating the correlation coefficient is: \[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \] where: \(x\) and \(y\) are the variables, \(n\) is the number of data points, \(\sum xy\) is the sum of the product of \(x\) and \(y\), \(\sum x\) and \(\sum y\) are the sums of \(x\) and \(y\) respectively, \(\sum x^2\) and \(\sum y^2\) are the sums of the squares of \(x\) and \(y\) respectively.
Step 2 :Given the data for lemon imports [232, 266, 357, 483, 534] and crash fatality rate [15.8, 15.7, 15.4, 15.2, 14.9], we can calculate the correlation coefficient.
Step 3 :The calculated linear correlation coefficient is \(r = -0.985\).
Step 4 :This negative value indicates a strong negative linear correlation between lemon imports and crash fatality rates.
Step 5 :However, correlation does not imply causation, so we cannot conclude that imported lemons cause car fatalities.
Step 6 :Final Answer: The linear correlation coefficient is \(r = \boxed{-0.985}\).