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Chapter 3: Q 9. (page 171)

Does fast driving waste fuel? How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort. Speed is measured in kilometers per hour and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled.

a. Make a scatterplot to display the relationship between speed and fuel consumption.

b. Describe the relationship between speed and fuel consumption.

Short Answer

Expert verified

Part (b) There is a decline in speed to 60km/hr and it has increased rapidly.

Part (a)

Step by step solution

01

Part (a) Step 1: Given information

The data set is:

02

Part (a) Step 2: Explanation

The scatter plot for the provided set can be constructed as:

03

Part (b) Step 1: Explanation

The scatter plot created in the previous section reveals that the variables fuel and speed have a non-linear relationship. The speed has dropped to 60 km/hr and is fast increasing.

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Most popular questions from this chapter

IQ and grades Exercise 3 (page 158) included the plot shown below of school grade point average (GPA) against IQ test score for 78seventh-grade students. (GPA was recorded on a 12-point scale with A+=12,A=11,A-=10,B+=9,...D-=1,F=0.) Calculation shows that the mean and standard deviation of the IQ scores areX炉=108.9and Sx=13.17For the GPAs, these values are Y=7.447andSy=2.10. The correlation between IQ and GPA is 0.6337

(a) Find the equation of the least-squares line for predicting GPA from IQ. Show your work.

(b) What percent of the observed variation in these students鈥� GPAs can be explained by the linear relationship between GPA and IQ?

(c) One student has an IQ of 103but a very low GPA of 0.53. Find and interpret the residual for this student

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between 鈥�1 and 1.

b. The least-squares regression line always goes through the point (x炉,y炉) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

Long strides The scatterplot shows the relationship between x = height of a student (in inches) and y = number of steps required to walk the length of a school hallway, along with the regression line y^=113.6鈭�0.921x

a. Calculate and interpret the residual for Kiana, who is 67 inches tall and took 49 steps to walk the hallway.

b. Matthew is 10 inches taller than Samantha. About how many fewer steps do you expect Matthew to take compared to Samantha?

Long jumps Here are the 40-yard-dash times (in seconds) and long-jump distances (in inches) for a small class of 12 students:

a. Sketch a scatterplot of the data using dash time as the explanatory variable.

b. Use technology to calculate the equation of the least-squares regression line for predicting the long-jump distance based on the dash time. Add the line to the scatterplot from part (a).

c. Explain why the line calculated in part (b) is called the 鈥渓east-squares鈥� regression line.
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