Question

shows the weight and fuel efficiency for each of 21 vehicles. also shown is the line of best fit for the data.
fuel efficiency (in miles per gallon)
(a) for these 21 vehicles, as weight increases, fuel efficiency tends to
(b) for these 21 vehicles, there is
correlation between weight and fuel efficiency.
(c) using the line of best fit, we would predict that a vehicle weighing 4000 pounds would have a fuel efficiency of approximately

Explanation:

Part (a)

Step 1: Analyze the trend of the scatter plot

The scatter plot shows the relationship between weight (x - axis) and fuel efficiency (y - axis). As the weight (in pounds) increases, we observe the general trend of the data points and the line of best fit. The line of best fit has a negative slope, which means as \(x\) (weight) increases, \(y\) (fuel efficiency) decreases. So, as weight increases, fuel efficiency tends to decrease.

Part (b)

Step 1: Determine the type of correlation

Since the line of best fit has a negative slope and the data points follow a pattern where an increase in weight is associated with a decrease in fuel efficiency, this is a negative correlation. Also, the points are relatively close to the line of best fit, so it is a strong negative correlation (or we can say negative, and if we consider the strength, it's a strong negative, but the main type of correlation here is negative).

Part (c)

Step 1: Locate \(x = 4000\) on the x - axis

We look at the line of best fit. When \(x = 4000\) (weight is 4000 pounds), we find the corresponding \(y\) - value on the line of best fit. From the graph, when we move up from \(x = 4000\) to the line of best fit and then to the y - axis (fuel efficiency in miles per gallon), we can see that the value is around 30 miles per gallon (we estimate by looking at the line of best fit: when weight is 4000 pounds, the line of best fit passes through a point where \(y\approx30\)).

Answer:

s:
(a) decrease
(b) negative (or strong negative)
(c) 30 (miles per gallon, approximate value from the line of best fit at \(x = 4000\))