Learn About Scatter Plots

Use the technology of your choice to do the following tasks. From the International Data Base, published by the U.S. Census Bureau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries. a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.

Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persistent Organic Pollutants in 2001: One study, published in 1972 by R. Risebrough, is titled “Effects of Environmental Pollutants Upon Animals Other Than Man”. In that study, 50 Anacapa pelican eggs were collected and measured for their shell thickness, in millimetres (mm), and concentration of PCBs, in parts per million (ppm). a) Obtain a scatterplot for the data. b) Decide whether finding a regressimz line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeissStats CD for those presidents who are not still living at the time of this writing. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be a great danger to natural ecosystems. In a study by R. W. Risebrough titled “Effects of Environmental Pollutants Upon Animals Other Than Man” (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443-463), 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)–(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

For each set of data below, draw a scatterplot and decide whether or not the data exhibits approximately periodic behaviour.

a) $\begin{array}{|cccccccccccccc|}\hline x& 0& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12\\ y& 0& 1& 1.4& 1& 0& -1& -1.4& -1& 0& 1& 1.4& 1& 0\\ \hline\end{array}$

 

b) $\begin{array}{|cccccc|}\hline x& 0& 1& 2& 3& 4\\ y& 4& 1& 0& 1& 4\\ \hline\end{array}$

 

c) $\begin{array}{|ccccccccc|}\hline x& 0& 0.5& 1.0& 1.5& 2.0& 2.5& 3.0& 3.5\\ y& 0& 1.9& 3.5& 4.5& 4.7& 4.3& 3.4& 2.4\\ \hline\end{array}$

 

d) $\begin{array}{|cccccccccccc|}\hline x& 0& 2& 3& 4& 5& 6& 7& 8& 9& 10& 12\\ y& 0& 4.7& 3.4& 1.7& 2.1& 5.2& 8.9& 10.9& 10.2& 8.4& 10.4\\ \hline\end{array}$

The U.S. Census Bureau publishes information on the population of the United States in Current Population Reports. The following table gives the resident U.S. population, in millions of persons, for the years 1990-2009. Forecast the U.S. population in the years 2010 and 2011

$\begin{array}{|cc|}\hline \text{Year}& \text{Population (millions)}\\ 1990& 250\\ 1991& 253\\ 1992& 257\\ 1993& 260\\ 1994& 263\\ 1995& 266\\ 1996& 269\\ 1997& 273\\ 1998& 276\\ 1999& 279\\ 2000& 282\\ 2001& 285\\ 2002& 288\\ 2003& 290\\ 2004& 293\\ 2005& 296\\ 2006& 299\\ 2007& 302\\ 2008& 304\\ 2009& 307\\ \hline\end{array}$

a) Obtain a scatterplot for the data.

b) Find and interpret the regression equation.

c) Mace the specified forecasts.

Heights and mid-parent heights are given for 18 college students. Draw a scatterplot for the data, using different symbols for males and females as instructed in part (b). Based on the scatterplot, would you say that the correlation between height and mid-parent height is higher for the females in the sample or for the males? Or are the correlation values about the same for males and females?

Use the technology of your choice to do the following tasks. The National Oceanic and Atmospheric Administration publishes temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inches) in July for 48 cities are on the WeissStats CD. For part (d), predict the average July precipitation of a city with an average July temperature of ${\displaystyle {83}^{\circ }F}$ a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.

The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for 121 vehicles. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Make a scatterplot of the data with two new points added.
a) ${\displaystyle 10\mathrm{\%}}$ return, 25 new birds.
b) ${\displaystyle 40\mathrm{\%}}$ return, 5 new birds.
Find two new correlations: for the original data plus Point A and for the original data plus Point B.

Use the sample data to construct a scatterplot.
Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation?
The table li sts che t sizes (di stance around chest in inches) and weights (pounds) of anesthetized bears that were measured.
$\begin{array}{|cccccccc|}\hline \text{Chest(in.)}& 26& 45& 54& 49& 35& 41& 41\\ \text{Weight(lb)}& 80& 344& 416& 348& 166& 220& 262\\ \hline\end{array}$

The ability to estimate the volume of a tree based on a simple measurement, such as the tree’s diameter, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines were reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Box Office Mojo collects and posts data on movie grosses. For a random sample of 50 movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. a) Obtain a scatterplot for the data. b) Decide whether finding a regressimz line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Does a higher state per capita income equate to a higher per capita beer consumption? From the document Survey of Current Business, published by the U.S. Bureau of Economic Analysis, and from the Brewer’s Almanac, published by the Beer Institute, we obtained data on personal income per capita, in thousands of dollars, and per capita beer consumption, in gallons, for the 50 states and Washington, D.C. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

There is a suspicion that time depends on distance. Make a scatterplot of time against distance, using separate symbols for each hand.

An issue of BARRON’S presented information on top wealth managers in the United States, based on individual clients with accounts of $1 million or more. Data were given for various variables, two of which were number of private client managers and private client assets. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)–(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.