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Chapter 3: Q. 3.2 (page 155)

The scatterplots below show four sets of real data:

(a) repeats the manatee plot in Figures

(b) shows the number of named tropical storms and the number predicted before the start of hurricane season each year between 1984and 2007by William Gray of Colorado State University;

(c) plots the healing rate in micrometers (millionths of a meter) per hour for the two front limbs of several newts in an experiment; and

(d) shows stock market performance in consecutive years over a 56-year period.

The scatterplot in (b) contains an outlier: the disastrous 2005season, which had 27named storms, including Hurricane Katrina. What effect would remove this point have on the correlation? Explain.

(a)

(b)

(c)

(d)

Short Answer

Expert verified

The association between the two variables would decline if the disastrous 2005season, which saw named storms, including Hurricane Katrina, was excluded.

Step by step solution

01

Given Information

The scatter plot is:

02

Explanation

the value 27is an outlier, Because it differs from the rest of the data points. This point implies that there is a positive linear relationship between the variables, and that if it is eliminated, the correlation between two variables will decrease.

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Most popular questions from this chapter

The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is

(a) the correlation.

(b) the slope of the least-squares regression line.

(c) the square of the correlation coefficient.

(d) the intercept of the least-squares regression line.

(e) the residual.

Acid rainResearchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for 150consecutive weeks. Acidity is measured by pH. Lower pH values show higher acidity. The researchers observed a linear pattern over time. They reported that the regression line pH鈭�=5.43-0.0053(weeks) 铿乼 the data well16.

(a) Identify the slope of the line and explain what it means in this setting.

(b) Identify the y-intercept of the line and explain what it means in this setting.

(c) According to the regression line, what was the pH at the end of this study?

When we standardize the values of a variable, the distribution of standardized values has a mean 0and a standard deviation 1Suppose we measure two variables Xand Yon 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 鈭�0.44We may conclude that

(a) the correlation will be 1/鈭�0.44

(b) the intercept will also be 鈭�0.44

(c) the intercept will be 1.0

(d) the correlation will be 1.0

(e) the correlation will also be 鈭�0.44

When it rains, it pours The figure below plots the record-high yearly precipitation in each state against that state鈥檚 record-high 24-hour precipitation. Hawaii is a high outlier, with a record-high yearly record of 704.83 inches of rain recorded at Kukui in 1982

(a) The correlation for all 50 states in the figure is 0.408 If we leave out Hawaii, would the correlation increase, decrease, or stay the same? Explain.

(b) Two least-squares lines are shown on the graph. One was calculated using all 50 states, and the other omits Hawaii. Which line is which? Explain.

(c) Explain how each of the following would affect the correlation, s, and the least-squares line:

  • Measuring record precipitation in feet instead of inches for both variables.
  • Switching the explanatory and response variables.

Merlins breeding Exercise 13 (page 160) gives data on the number of breeding pairs of merlins in an isolated area in each of nine years and the percent of males who returned the next year. The data show that the percent returning is lower after successful breeding seasons and that the relationship is roughly linear. The figure below shows the Minitab regression output for these data.

(a) What is the equation of the least-squares regression line for predicting the percent of males that

return from the number of breeding pairs? Use the equation to predict the percent of returning males after a season with 30 breeding pairs.

(b) What percent of the year-to-year variation in the percent of returning males is explained by the straight-line relationship with a number of breeding pairs the previous year?

(c) Use the information in the figure to find the correlation r between the percent of males that return and the number of breeding pairs. How do you know whether the sign of r is + or 鈭�?

(d) Interpret the value of s in this setting.
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