find the regression equation

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? lemon imports 235,265,355,468,511 crash fatality rate 16,15.7,15.4,15.4,15

Answer 1

To find the best predicted crash fatality rate based on lemon imports, we use a linear regression equation. The general form of the equation is y = mx + b, where y is the dependent variable (crash fatality rate), x is the independent variable (lemon imports), m is the slope, and b is the y-intercept.

Given Data:

1. Lemon Imports (metric tons): [235, 265, 355, 468, 511]
2. Crash Fatality Rate (per 100,000 people): [16, 15.7, 15.4, 15.4, 15]

We perform linear regression and obtain the following equation: Crash Fatality Rate = -0.00284 * Lemon Imports + 16.54

The R-value is approximately -0.921, suggesting a strong negative correlation. The p-value is 0.0263, which is less than the significance level of 0.05, making the model statistically significant.

For a year with 400 metric tons of lemon imports, we use the equation to predict: Crash Fatality Rate = -0.00284 * 400 + 16.54 The best predicted crash fatality rate is approximately 15.41 per 100,000 people.

While the model is statistically significant, it's crucial to remember that correlation does not imply causation. The prediction should be scrutinized for real-world applicability.