Chapter 3: Q 74. (page 209)
By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is
a. greater than zero.
b. less than zero.
c. 0.93.
d. 6.4.
e. Can’t tell without seeing the data.
The correct option is (a) greater than zero.
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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 students
When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least squares regression line. Suppose the slope of the least-squares regression line is 20.44. We may conclude that
a. the intercept will also be −0.44.
b. the intercept will be 1.0.
c. the correlation will be 1/−0.44.
d. the correlation will be 1.0.
e. the correlation will also be −0.44.
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.
Long-term records from the Serengeti National Park in Tanzania show interesting ecological relationships. When wildebeest are more abundant, they graze the grass more heavily, so there are fewer fires and more trees grow. Lions feed more successfully when there are more trees, so the lion population increases. Researchers collected data on one part of this cycle, wildebeest abundance (in thousands of animals) and the percent of the grass area burned in the same year. The results of a least-squares regression on the data are shown here. 
a. Is a linear model appropriate for describing the relationship between wildebeest abundance and percent of grass area burned? Explain.
b. Give the equation of the least-squares regression line. Be sure to define any variables you use.
c. Interpret the slope. Does the value of the y-intercept have meaning in this context? If so, interpret the y-intercept. If not, explain why.
d. Interpret the standard deviation of the residuals and r2.
Longer strides In Exercise 43, we summarized the relationship between x =
height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6−0.921x. For this
model, technology gives s = 3.50 and r2 = 0.399.
a. Interpret the value of s.
b. Interpret the value of r2.
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