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Chapter 3: Q. 35 (page 191)
You use the same bar of soap to shower each morning. The bar weighs grams when it is new. Its weight goes down by grams per day on average. What is the equation of the regression line for predicting weight from days of use?
The equation is.
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55. Bird colonies Refer to Exercise .
(a) Use your calculator to make a residual plot. Describe what this graph tells you about how well the line fits the data.
(b) Which point has the largest residual? Explain what this residual means in context.
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 and by 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 -year period.
For each graph, estimate the correlation r. Then interpret the value of r in context.
(a)
(b)
(c)
(d)
What affects correlation? Make a scatterplot of the following data:
The correlation for these data is . What is responsible for reducing the correlation to this value despite a strong straight-line relationship between and in most of the observations?
Data on dating Refer to Exercise 20.
(a) How would change if all the men were inches shorter than the heights given in the table? Does the correlation tell us if women tend to date men taller than themselves?
(b) If heights were measured in centimeters rather than inches, how would the correlation change? (There are centimeters in an inch.)
Does social rejection hurt? Exercise (page ) gives data from a study that shows that social exclusion causes 鈥渞eal pain.鈥� That is, activity in an area of the brain that responds to physical pain goes up as distress from social exclusion goes up. A scatterplot shows a moderately strong, linear relationship. The figure below shows the Minitab regression output for these data.
(a) What is the equation of the least-squares regression line for predicting brain activity from social distress score? Use the equation to predict brain activity for social distress score of
(b) What percent of the variation in brain activity among these subjects is explained by the straight-line relationship with the social distress score?
(c) Use the information in the figure to find the correlation r between social distress score and brain
activity. 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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