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Chapter 3: Q.1.3 (page 167)
Predict the rat鈥檚 weight after weeks. Show your work
The rat's weight after weeks grams
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Joan is concerned about the amount of energy she uses to heat her home. The graph below plots the mean number of cubic feet of gas per day that Joan used each month against the average temperature that month (in degrees Fahrenheit) for one heating season.
(a) Does the plot show a positive or negative association between the variables? Why does this make sense?
(b) What is the form of the relationship? Is it very strong? Explain your answers.
(c) Explain what the point at the bottom right of the plot represents.
Merlins breeding The percent of an animal species in the wild that survives to breed again is often lower following a successful breeding season. A study of merlins (small falcons) in northern Sweden observed the number of breeding pairs in an isolated area and the percent of males (banded for identification) that returned the next breeding season. Here are data for nine years:
Investigate the relationship between breeding pairs and percent return. Follow the four-step process.
An eccentric professor believes that a child with an IQ should have a reading test score and that the reading score should increase by a point for every additional point of IQ. What is the equation of the professor鈥檚 regression line for predicting reading scores from IQ?
Hot dogs Are hot dogs that are high in calories also high in salt? The figure below is a scatterplot of the calories and salt content (measured as milligrams of sodium) in brands of meat hot dogs.
(a) The correlation for these data is . Explain what this value means.
(b) What effect would removing the hot dog brand with the lowest calorie content have on the correlation? Justify your answer.
Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:
(a) Make a scatterplot. Do you think that all five specimens come from the same species? Explain.
(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for . Explain how your value for matches your graph in (a).
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