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Magazine Chapter 2: Q7 (page 75)
Scatterplot. In Exercises 5鈥�8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation?
Car Weight and Fuel Consumption The table lists weights (pounds) and highway fuel consumption amounts (mpg) for a Hyundai Elantra, Nissan Altima, VW Passat, Buick Lucerne, Mercury Grand Marquis, Honda Civic, and Honda Accord.
Weight (lb) | 2895 | 3215 | 3465 | 4095 | 4180 |
Highway (mpg) | 33 | 31 | 29 | 25 | 24 |
Short Answer
The scatterplot is constructed as shown below:
By observing the scatterplot, it can be seen that the points lie close to a straight-line pattern. Thus, the two variables, the weight of the car and highway fuel consumption, are linearly correlated.
Step by step solution
Given information
Two variables, namely the weight (lb) of cars and the corresponding highway fuel consumption amounts (mpg) are recorded for different cars.
Weight(lb) | 2895 | 3215 | 3465 | 4095 | 4180 | 2740 | 3270 |
Highway(mpg) | 33 | 31 | 29 | 25 | 24 | 36 | 30 |
Construct the scatterplot
Scatterplots use observations in paired form from quantitative variables to represent in the graph.
Use the following steps to plot a scatterplot between weight andfuel comsumption amounts:
- Consider x as weight (lb) and y as highway (mpg).
- Mark the values 2500, 3000, and so on till 4500 on the horizontal axis.
- Mark the values 20, 25, and so on till 40 on the vertical axis.
- Plot the points on the graph corresponding to the pairs of values for the two variables.
- Label the horizontal axis as 鈥淲eight(lb)鈥� and the vertical axis as 鈥淗ighway(mpg).鈥�
The following scatterplot is generated:
Analyze the scatterplot
The scatterplot is used to conclude the nature of the association between the observations of two variables.
It can be observed that the points lie close to a straight-line pattern such that with an increase in weight of the car, the fuel consumption decreases.
Therefore, it can be concluded that the weight of cars and highway fuel consumption are linearly related in a negative direction.
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