Determine the line of aggression I used to find the best predicted new mileage rating of a four-wheel-drive vehicle given that the old rating is 19 miles per gallon. Old 16, 27, 17, 33, 28, 24, 18. New, 15, 24, 15, 29, 25, 22, 16
The line of regression used to find the best predicted new mileage rating for a four-wheel-drive vehicle given an old rating of 19 miles per gallon is the simple linear regression line.
Using the old and new mileage ratings provided, the calculated line of regression predicts the new mileage rating based on the old rating. The formula for a simple linear regression line is y = mx + b, where y is the predicted new rating, x is the old rating, m is the slope, and b is the y-intercept.
To calculate the line of regression using the given data:
Old: 16, 27, 17, 33, 28, 24, 18
New: 15, 24, 15, 29, 25, 22, 16
The correlation coefficient for the data is r = 0.893, indicating a strong positive linear relationship between the old and new mileage ratings.
Slope (m) = r * (σy/σx) = 0.893 * (4.04/6.08) = 0.5956
Y-intercept (b) = mean(y) - (m * mean(x)) = 22.57 - (0.5956 * 23.43) = 8.19
Therefore, the line of regression for predicting the new mileage rating based on the old rating is:
New rating = 0.5956 * Old rating + 8.19
Using this regression line, we can predict the new mileage rating for an old rating of 19 miles per gallon:
New rating = 0.5956 * 19 + 8.19 = 19.7
Therefore, based on the regression analysis, the best predicted new mileage rating for a four-wheel-drive vehicle with an old rating of 19 miles per gallon is approximately 19.7 miles per gallon.