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Chapter 3: Q 54. (page 205)

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

Short Answer

Expert verified

The pattern does not appear to include considerable curvature, implying that the linear model is adequate.

Step by step solution

01

Given information

02

Explanation

Now we must plot the dash time in seconds and the long-jump distance in inches on a residual plot. To make it, we'll utilize a calculator, such as a Ti83/84-calculator. To get to plot 1start by pressing 2nd>Y=and then entering. Then make sure that On is selected and that the first graph type is chosen. L1comes after Xlistand RESID comes after YlistAs a result of pressing GRAPH at the end, we get the following:

This suggests that the point pattern looks to be random in the scatterplot and that the pattern does not appear to include considerable curvature, implying that the linear model is adequate.

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Most popular questions from this chapter

Late bloomers? Japanese cherry trees tend to blossom early when spring weather is warm and later when spring weather is cool. Here are some data on the average March temperature (in degrees Celsius) and the day in April when the first cherry blossom appeared over a 24-year period:

a. Make a well-labeled scatterplot that’s suitable for predicting when the cherry trees will blossom from the temperature. Which variable did you choose as the explanatory variable? Explain your reasoning.

b. Use technology to calculate the correlation and the equation of the least-squares regression line. Interpret the slope and y-intercept of the line in this setting.

c. Suppose that the average March temperature this year was 8.2°C. Would you be willing to use the equation in part (b) to predict the date of the first blossom? Explain your reasoning.

d. Calculate and interpret the residual for the year when the average March temperature was 4.5°C.

e. Use technology to help construct a residual plot. Describe what you see.

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.

Teenagers and corn yield Identify the explanatory variable and the response variable for the following relationships, if possible. Explain your reasoning.

a. The height and arm span of a sample of 50 teenagers.

b. The yield of corn in bushels per acre and the amount of rain in the growing season.

Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of 12 women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body mass is an

important influence on metabolic rate.

a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.

b. Describe the relationship between lean body mass and metabolic rate.

Oh, that smarts! Infants who cry easily may be more easily stimulated than others. This may be a sign of a higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days old and their IQ test scores at age 3 years. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. The correlation for these data is r=0.45.16 Interpret the correlation.
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