# Scatterplots, Coefficients, and Regression Analysis

I need help with the attached. It deals with scatter plots.

Thank you for you help.

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1. A value of r = -0.851 shows that there is very little relationship between the two variables being compared.

2. A value of r = 0.158 shows that there is very little relationship between the two variables being compared.

3. If a correlation coefficient of r = 0.642 was found between two variables in a sample of paired data that were measured in feet, the value of r would change if the data were converted to inches and r was computed again.

4. Bear Chest Size and Weight. Listed below are the chest sizes (in inches) and weights (in pounds) of randomly selected bears that were anesthetized and measured (based on data from Gary Alt and Minitab, Inc.). Because it is much more difficult to weigh a bear than to measure its chest size, the presence of a correlation could lead to a method for estimating weight based on chest size. Is there a linear correlation between chest size and weight?

5. Buying a TV Audience. The New York Post published the annual salaries (in millions) and the number of viewers (in millions), with results given below for Oprah Winfrey, David Letterman, Jay Leno, Kelsey Grammer, Barbara Walters, Dan Rather, James Gandolfini, and Susan Lucci, respectively. Is there a correlation between salary and number of viewers? Which of the listed stars has the lowest cost per viewer? Highest cost per viewer?

6. Temperatures and marathons. In "The Effects of Temperature on Marathon Runner's Performance," by David Martin and John Buoncristiani (Chance, Vol. 12, No. 4), high temperatures and times (in minutes) were given for women who won the New York City marathon in recent years. Results are listed below. Is there a correlation between temperature and winning time? Does it appear that winning times are affected by temperature?

7. Use the same data sets as Exercises 13-32 in Section 10-2. In each case, find the regression equation, letting the first variable be the independent (x) variable. Find the indicated predicted values.

Bear Chest Size and Weight. Find the best predicted weight (in pounds) of a bear with a chest size of 50 in.

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#### Solution Summary

This is a set of solutions for correlation coefficients, scatter plots, linear correlations, and regression analyses.

2 Sets of Problems - Regression : Correlation Coefficient, Scatterplot, Least-Squares and Data Analysis

(See attached file for full problem description)

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47. In general, people tend to live longer in countries that have a greater supply of food. Listed below is the 1997 daily calorie supply and 2000 life expectancy at birth for 10 randomly selected countries.

Country Calories (x) Life expectancy (y)

Afghanistan 1523 43

Belize 2862 74

Cambodia 1974 56

France 3551 79

India 2415 64

Mexico 3137 73

New Zealand 3405 78

Peru 2310 70

Sweden 3160 80

U.S. 3642 78

a. Find the coefficient of correlation. Do the data seem to fit a straight line?

b. Draw a scatterplot of the data. Combining this with your results from part a, do the data seem to fit a straight line?

c. Find the equation for the least squares line.

d. Use your answer from part c to predict the life expectancy in the United Kingdom, which has a daily calorie supply of 3237. Compare your answer with the actual value of 78 years.

e. Briefly explain why countries with a higher daily calorie supply might tend to have a longer life expectancy.

f. Find the coefficient of correlation and least squares line using data for a larger sample of countries, as found in an almanac or other reference. Is the result in general agreement with the previous results?

51. In general, the larger a state's population, the more its governor earns. Listed below are the estimated 2001 populations (in millions) and the salary of the governor (in thousands of dollars) for 8 randomly selected states.

a. Find the coefficient of correlation. Do the data seem to fit a straight line?

b. Draw a scatterplot of the data. Compare this with your answer from part a.

c. Find the equation for the least squares line.

d. Based on your answer to part c, how much does a governor's salary increase, on average, for each additional million in population?

e. Use your answer from part c to predict the governor's salary in your state. Based on your answers from parts a and b, would this prediction be very accurate? Compare with the actual salary, as listed in the almanac or other reference.

f. Find the coefficient of correlation and least squares line using data for all 50 states, as found in an almanac or other reference. Is the resulting general agreement with the previous results?

State AZ DE MD MA NY PA TN WY

Population(x) 5.31 .80 5.38 6.38 19.01 12.29 5.74 .49

Governor's 95 114 120 135 179 142 85 95

Salary (y)

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(See attached file for full problem description)