Question

question 1 - 12
a scientist is studying the relationship between the weight of a vehicle, in tons, and its energy efficiency levels, in kilometers per gigajoule (km/gj). the scientist studied several vehicles of different weights for a year. the results are shown on the scatter plot below with the line of best fit, which can be described by the model y = -20.3x + 326.
vehicle energy efficiency
the residuals based on the scatter plot are shown in the table below.
weight of vehicle (tons)\tenergy efficiency levels (km/gj)\tresidual value
2\t288.2\t2.8
3\t250.4\t-14.7
6\t199.7\t-4.5
7\t186.2\t2.3
8\t187.9\t24.3
11\t101.3\t-1.4
12\t100.2\t17.8
14\t39.8\t-2
select the statement that best describes the direction of the correlation of the line of best fit as it relates to the weight of the vehicle and its energy efficiency levels.
strong positive linear relationship
strong negative linear relationship
weak positive linear relationship
weak negative linear relationship

Explanation:

The line of best - fit equation is \(y=-20.3x + 326\), where the slope is negative (\(-20.3\)). A negative slope indicates that as the weight of the vehicle (\(x\)) increases, the energy efficiency levels (\(y\)) decrease. Also, the points on the scatter - plot seem to follow the line of best - fit relatively closely, suggesting a strong relationship.

Answer:

strong negative linear relationship