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Chapter 3: Q.57 (page 193)
57. Bird colonies Refer to Exercises and . For the regression you performed earlier, and . Explain what each of these values means in this setting.
The values are expected to differ by about from the actual values.
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Born to be old? Is there a relationship between the gestational period (time from conception to birth) of an animal and its average life span? The figure shows a scatterplot of the gestational period and average life span for species of animals.
(a) Describe the direction, form, and strength of the scatterplot.
(b) Three 鈥渦nusual鈥� points are labeled on the graph: Point is for the hippopotamus, Point is for the giraffe, and Point is for the Asian elephant. In what way is each of these animals 鈥渦nusual鈥�?
Southern education For a long time, the South has lagged behind the rest of the United States in the performance of its schools. Efforts to improve education have reduced the gap. We wonder if the South stands out in our study of state average SAT Math scores.
The figure below enhances the scatterplot in Figure (page ) by plotting southern states in red.
(a) What does the graph suggest about the southern states?
(b) The point for West Virginia is labeled in the graph. Explain how this state is an outlier.
Acid rainResearchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for consecutive 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 =(weeks) 铿乼 the data well.
(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?
Managing diabetes People with diabetes measure their fasting plasma glucose (FPG; measured in units of milligrams per milliliter) after fasting for at least 8 hours. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose
molecule attached. It measures average exposure to glucose over a period of several months. The table below gives data on both HbA and FPG for diabetics five months after they had completed a diabetes education class.
(a) Make a scatterplot with HbA as the explanatory variable. There is a positive linear relationship, but it is surprisingly weak.
(b) Subject is an outlier in the y-direction. Subject is an outlier in the x-direction. Find the correlation for all subjects, for all except Subject and
for all except Subject Are either or both of these subjects influential for the correlation? Explain in simple language why r changes in opposite directions when we remove each of these points.
(c) Add three regression lines for predicting FPG from HbA to your scatterplot: for all subjects, for all except Subject and for all except Subject
Is either Subject or Subject strongly influential for the least-squares line? Explain in simple language what features of the scatterplot explain the degree of influence.
The fraction of the variation in the values of that is explained by the least-squares regression of on 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.
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