Question

the scatter plot shows the weight and fuel efficiency for each of 25 vehicles. also shown is the line of best fit for the data. fill in the blanks below. (a) for these 25 vehicles, as weight increases, fuel efficiency tends to decrease. (b) for these 25 vehicles, there is a negative correlation between weight and fuel efficiency. (c) using the line of best fit, we would predict that a vehicle weighing 3500 pounds would have a fuel efficiency of approximately select

Explanation:

Step1: Analyze the scatter - plot trend

Looking at the scatter - plot, as the \(x\) - value (weight) increases, the \(y\) - value (fuel efficiency) moves downwards. So, for part (a), as weight increases, fuel efficiency tends to decrease.

Step2: Determine the correlation type

Since an increase in one variable (weight) is associated with a decrease in the other variable (fuel efficiency), the correlation is negative. So, for part (b), there is a negative correlation.

Step3: Estimate the fuel efficiency using the line of best fit

Locate \(x = 3500\) on the \(x\) - axis (weight axis). Then, move vertically until you reach the line of best fit. From the line of best fit, move horizontally to the \(y\) - axis (fuel efficiency axis). By visual inspection of the scatter - plot (assuming standard scale), when \(x=3500\), \(y\approx30\) (miles per gallon).

Answer:

(a) decrease
(b) a negative
(c) 30 miles per gallon