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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^=11.058–0.01466x. 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⏜=11.058−0.01466x

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

Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value.”

Which of the following gives a correct interpretation of s in this setting?

a. For every 1°C increase in temperature, fish activity is predicted to increase by 4.785 units.

b. The typical distance of the temperature readings from their mean is about 4.785°C.

c. The typical distance of the activity level ratings from the least-squares line is about 4.785 units.

d. The typical distance of the activity level readings from their mean is about 4.785 units.

e. At a temperature of 0°C, this model predicts an activity level of 4.785 units.

Coral reefs and cell phones Identify the explanatory variable and the

response variable for the following relationships, if possible. Explain your reasoning.

a. The weight gain of corals in aquariums where the water temperature is controlled at different levels

b. The number of text messages sent and the number of phone calls made in a sample of 100students

Windy city Is it possible to use temperature to predict wind speed? Here is a scatterplot showing the average temperature (in degrees Fahrenheit) and average wind speed (in miles per hour) for 365 consecutive days at O’Hare International Airport in Chicago.14 Is r>0 or r<0? Closer to r=0orr=±1? Explain your reasoning.

Managing diabetes People with diabetes measure their fasting plasma glucose (FPG, measured in milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months. The table gives data on both HbA and FPG for 18 diabetics five months after they had completed a diabetes education class.

a. Make a scatterplot with HbA as the explanatory variable. Describe what you see.

b. Subject 18 is an outlier in the x-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.

c. Subject 15 is an outlier in the y-direction. What effect do you think this subject has on the correlation? What effect do you think this subject has on the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this subject to confirm your answer.

In addition to the regression line, the report on the Mumbai measurements says that r2 =0.95. This suggests that

a. although arm span and height are correlated, arm span does not predict height very accurately.

b. height increases by 0.95=0.97 cm for each additional centimeter of arm

span.

c. 95% of the relationship between height and arm span is accounted for by the regression line.

d. 95% of the variation in height is accounted for by the regression line with x = arm span. e. 95% of the height measurements are accounted for by the regression line with x = arm span.
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