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Regression : Correlation Coefficient, Scatterplot, Least-Squares and Data Analysis

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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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Solution Summary

Linear Regression, Correlation Coefficient, Scatterplot, Least-Squares and Data Analysis are investigated for two problem sets. The solution is detailed and well presented. Graphs are included.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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