MATH 225N Week 8 Assignment; Performing Linear Regressions with Technology

1. Question: An economist is studying the link between the total value of a country's exports and that country's gross domestic product, or GDP. The economist recorded the GDP and Export value (in millions of $'s) for 30 nations for the same fiscal year. This sample data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. 2. Question: The table below shows data on annual expenditure, x(in dollars), on recreation and annual income, y (in dollars), of 20 families. Use Excel to find the best fit linear regression equation. Round the slope and intercept to the nearest integer. 3. Question: Jorge is an economist trying to understand whether there is a strong link between CEO compensation and corporate revenue. He gathered data including the CEO compensation for 30randomly selected corporations for a particular year as well as the corporate revenue of those corporations for the same year. The data Jorge gathered are provided in the accompanying data table. Use Excel to calculate the correlation coefficient rbetween the two data sets. Round your answer to two decimal places. 4. Question: In the following table, the age (in years) of the respondents is given as the x value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places. 5. Question: The heights (in inches) and weights (in pounds) of 25 baseball players are given below. Use Excel to find the best fit linear regression equation, where height is the explanatory variable. Round the slope and intercept to two decimal places. 6. Question: The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places. 7. Question: An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the absolute magnitude or MVand stellar mass or M⊙ for 30 stars. The absolute magnitude of a star is the intensity of light that would be observed from the star at a distance of 10 parsecs from the star. This is measured in terms of a particular band of the light spectrum, indicated by the subscript letter, which in this case is Vfor the visual light spectrum. The scale is logarithmic and an MVthat is 1 less than another comes from a star that is 10 times more luminous than the other. The stellar mass of a star is how many times the sun's mass it has. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places. 8. Question: An economist is trying to understand whether there is a strong link between CEO pay ratio and corporate revenue. The economist gathered data including the CEO pay ratio and corporate revenue for 30 companies for a particular year. The pay ratio data is reported by the companies and represents the ratio of CEO compensation to the median employee salary. The data are provided below. Use Excel to calculate the correlation coefficient rbetween the two data sets. Round your answer to two decimal places. 9. Question: An energy economist studying the growth and decay of both the coal and natural gas industries wanted to leverage data collected by environmental scientists. Particularly, the economist wanted to study the link between the total yearly carbon emissions from both energy sources. They looked at 30 years of total yearly carbon emissions for a particular nation (measured in million metric tons of carbon dioxide) for both forms of energy. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. 10. Question: An owner of a large car lot believes that fuel prices are going to rise significantly and wonders how this rise might affect demand for the high performance vehicles. Specifically, the owner is investigating a link between how fast a car can go from 0 to 60 miles per hour (measured in seconds) and the car's economy as measured in miles traveled per gallon used (mpg). If fast cars, which are normally high in demand, are associated with higher mpg then there will be much less demand if gas prices rise as predicted. The owner gathers data on 20vehicles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.