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Chapter 12: Q. 2 (page 787)

Predicting high temperatures Using the daily high and low temperature readings at Chicago’s O’Hare International Airport for an entire year, a meteorologist made a scatterplot relating y=high temperature to x=low temperature, both in degrees Fahrenheit. After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be μy=16.6+1.02xwith σ=6.64°F. a. According to the population regression line, what is the average high temperature on days when the low temperature is 40°F? b. About what percent of days with a low temperature of 40°F have a high temperature greater than 70°F? c. If the meteorologist used a random sample of 10 days to calculate the regression line instead of using all the days in the year, would the slope of the sample regression line be exactly 1.02? Explain your answer.

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Most popular questions from this chapter

The professor swims Here are data on the time (in minutes) Professor Moore takes to swim 2000yards and his pulse rate (beats per minute) after swimming on a random sample of 23days:

Is there convincing evidence of a negative linear relationship between Professor Moore’s swim time and his pulse rate in the population of days on which he swims2000yards?

R12.5 Light intensity In a physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. Here is a scatterplot of the data. Note that a candela is a unit of luminous intensity in the International System of Units.

Physics textbooks suggest that the relationship between light intensity y and distance x should follow an “inverse square law,” that is, a power law model of the form y=ax-2=a1x2. We transformed the distance measurements by squaring them and then taking their reciprocals. Here is some computer output and a residual plot from a least-squares regression analysis of the transformed data. Note that the horizontal axis on the residual plot displays predicted light intensity.

a. Did this transformation achieve linearity? Give appropriate evidence to justify your answer.
b. What is the equation of the least-squares regression line? Define any variables you use.
c. Predict the intensity of a 100-watt bulb at a distance of 2.1 meters.

A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were available. The following table displays the data

Is there convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries?

Does how long young children remain at the lunch table help predict how much they eat? Here are data on a random sample of 20toddlers observed over several months. “Time” is the average number of minutes a child spent at the table when lunch was served. “Calories” is the average number of calories the child consumed during lunch, calculated from careful observation of what the child ate each day.


Here is some computer output from a least-squares regression analysis of these data. Do these data provide convincing evidence at the α=0.01α=0.01level of a linear relationship between time at the table and calories consumed in the population of toddlers?


PredictorCoefSECoefTPConstant560.6529.3719.090.000Time−3.07710.8498−3.620.002S=23.3980R-Sq=42.1%R-Sq(adj)=38.9%

T12.9 Which of the following would provide evidence that a power model of the form y=axp, wherep≠0and p≠1, describes the relationship between a response variable y and an explanatory variable x?
a. A scatterplot of y versus x looks approximately linear.
b. A scatterplot of Iny versus x looks approximately linear.
c. A scatterplot of y versus lnx looks approximately linear.
d. A scatterplot of Iny versus lnx looks approximately linear.
e. None of these

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