Question

How does the fuel consumption of a car change as its speed increases? The table contains data for a 2014 Chevrolet Cruze Turbo Diesel. Speed is measured in miles per hour, and fuel consumption is measured in miles per gallon. Speed 10 20 30 40 50 60 70 80 Fuel 38.1 54.0 68.4 63.6 60.5 55.4 50.6 43.8 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!

(a) Which is the correct scatterplot? Which is the explanatory variable?

The scatterplot is entitled Speed is the explanatory variable.

The scatterplot is entitled Fuel is the explanatory variable.

The scatterplot is entitled Fuel is the explanatory variable.

The scatterplot is entitled Speed is the explanatory variable.

(b) The form of the relationship is not linear. Select the best explanation of why the form of the relationship makes sense. There is no particular form to the relationship. This makes sense because the fuel efficiency is better explained by other factors besides speed; for example, temperature, rpm, and wind speed. The relationship is curved — downwards overall, but with a pair of outliers. This makes sense because neither a perfect fit nor a straight line should be expected for such a complex machine. The relationship is curved — high in the middle, lower at the extremes. This makes sense because most speed limits in the city are around the speed where the peak occurs in the graph. The relationship is curved — high in the middle, lower at the extremes. This makes sense because engines are designed for specific speed, temperature, and rpm ranges. Driving out of these ranges goes against the fundamental design of the engine, leading to less efficient use of fuel.

(c) It does not make sense to describe the variables as either positively associated or negatively associated. Why?

The association between fuel consumption and speed is not inherently positive or negative, since the choice of driving speed is influenced more strongly by other factors such as safety and speed limit. Below‑average (that is, bad) values of fuel consumption are found with both low and high values of speed.

There is no particular association between the variables at all, so it is certainly neither positive nor negative.

Above‑average (that is, good) values of fuel consumption are found with both low and high values of speed.

(d) Is the relationship reasonably strong or quite weak? Select the best explanation for your answer.

The relationship is very strong — a simple curve could be drawn such that there is little scatter around it, so that curve would be very useful for prediction.

The relationship is very strong — a well‑fitting curve would have a positive trend in most ? ‑intervals.

The relationship is very weak — a well‑fitting curve would have a negative trend in most ? ‑intervals.

The relationship is quite weak — any simple curve drawn would be such that there is wide scatter around it, so that curve would not be very useful for prediction.

Answer 1