Question

The equation of the linear regression line represents the relationship between the number of laps a person can swim, x, and the number of minutes a person can run, y.
y=5/2x+6

What does the slope of the line represent?
 


A. For every 2 laps that a person can swim, the number of minutes they can run increases by 5.

B. For every 5 laps that a person can swim, the number of minutes they can run decreases by 2.

C. For every 5 laps that a person can swim, the number of minutes they can run increases by 2.

D. For every 2 laps that a person can swim, the number of minutes they can run decreases by 5.

Answer 1

The most common method for fitting a regression line is the method of least-squares. This method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the vertical deviations from each data point to the line (if a point lies on the fitted line exactly, then its vertical deviation is 0). Because the deviations are first squared, then summed, there are no cancellations between positive and negative values.ExampleThe dataset "Televisions, Physicians, and Life Expectancy" contains, among other variables, the number of people per television set and the number of people per physician for 40 countries. Since both variables probably reflect the level of wealth in each country, it is reasonable to assume that there is some positive association between them. After removing 8 countries with missing values from the dataset, the remaining 32 countries have a correlation coefficient of 0.852 for number of people per television set and number of people per physician. The r² value is 0.726 (the square of the correlation coefficient), indicating that 72.6% of the variation in one variable may be explained by the other. (Note: see correlation for more detail.) Suppose we choose to consider number of people per television set as the explanatory variable, and number of people per physician as the dependent variable. Using the MINITAB "REGRESS" command gives the following results:

The regression equation is People.Phys. = 1019 + 56.2 People.Tel.