1) The average gasoline price per gallon and the cost of a barrel of oil are shown for a random selection of weeks from 2009-2010. Is there a linear relationship between the variables?
Oil: 46.25, 37.51, 78, 75.39, 84.88, and 73.78
Gasoline: 2.197, 2.182, 2.987, 3.015, 3.109, and 3
2) An environmentalist wants to determine the relationships between the numbers of forest fires over the year and the number of acres burned. The data for 8 recent years are shown. Describe the relationship.
Number of fires x: 72, 69, 58, 47, 84, 62, 57, and 45
Number of acres burned y: 62, 42, 19, 26, 51, 15, 30, and 15
3) An economic student wishes to see if there is a relationship between the amount of state debt per capita and the amount of tax capita at the state level. Based on the following data, can she or he conclude that per capita debt and per capita taxes are related? Both amounts are in dollars and represent five randomly selected states.
Per capita debt x: 1924, 907, 1445, 1608, 661
Per capita tax y: 1685, 1838, 1734, 1842, and 1317
4) Is there a relationship between the life expectancy for men and life expectancy for women in a given country? A random sample of non-industrialized countries was selected, and the life expectancy in years is listed for both men and women. Are the variables linearly related?
Men: 59.7, 72.9, 41.9, 46.2, 50.3, and 43.2
Women: 63.8, 77.8, 44.5, 48.3, 54, and 43.6
5) What is the symbol for the slope? For the y' intercept?
6) When all the points fall on the regression line, what is the value of the correlation coefficient?
7) As the value of the correlation coefficient increases from 0 to 1, or decreases from 0 to -1, how do the points of the scatter plot fit the regression line?
8) When the value of r is not significant, what value should be used to predict y?