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Chapter 3: Q 48. (page 204)

Driving speed and fuel consumption Exercise 9 (page 171) gives data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured in liters of gasoline per 100 kilometers driven, and speed is measured in kilometers per hour. A statistical software package gives the least-squares regression line y^=11.058鈥�0.01466x. Use the residual plot to determine if this linear model is appropriate.

Short Answer

Expert verified

No, it is not appropriate.

Step by step solution

01

Given information

The figure is:

02

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

03

Explanation

The regression equation is:

y铃�=11.058鈭�0.01466x

The data points on the residual plot should follow a linear pattern, which is an important property of an adequate linear regression model. The data points in the presented residual plot do not form a linear pattern, making the model incorrect. Simply put, the existence of curvature in the residual plot indicates that the model is ineffective.

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Most popular questions from this chapter

The scatterplot shows the relationship between the number of people per television set and the number of people per physician for 40 countries, along with the least-squares regression line. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. Which of the following is correct?

a. Increasing the number of TVs in a country will attract more doctors.

b. The slope of the least-squares regression line is less than 1.

c. The correlation is greater than 1.

d. The point for Ethiopia is decreasing the slope of the least-squares regression line.

e. Ethiopia has more people per doctor than expected, based on how many people it has per TV.

More Starbucks In Exercises 6 and 12, you described the relationship between fat (on Page Number: 204 grams) and the number of calories in products sold at Starbucks. The scatterplot shows this relationship, along with two regression lines. The regression line for the food products (blue squares) is y^=170+11.8x. The regression line for the drink products

(black dots) is y^=88+24.5x

a. How do the regression lines compare?

b. How many more calories do you expect to find in a food item with 5 grams of fat compared to a drink item with 5 grams of fat?

More long jumps Refer to Exercise 52. Use technology to create a residual plot. Sketch the residual plot and explain what information it provides.

Residual gas Refer to Exercise 38. During March, the average temperature was 46.4掳F and Joan used an average of 490 cubic feet of gas per day. Calculate and interpret the residual for this month.

The following graph plots the gas mileage (in miles per gallon) of various cars from the same model year versus the weight of these cars (in thousands of pounds). The points marked with red dots correspond to cars made in Japan. From this plot, we may conclude that

a. there is a positive association between weight and gas mileage for Japanese cars.

b. the correlation between weight and gas mileage for all the cars is close to 1.

c. there is little difference between Japanese cars and cars made in other countries.

d. Japanese cars tend to be lighter in weight than other cars.

e. Japanese cars tend to get worse gas mileage than other cars.
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