1. The data show a downwards trend that is roughly linear. Cities in which the average number of work hours per month is high tend to have low average teachers' salaries.Stats 110B Quiz 3 April 30, 1999
NAME:
Shown below (next page) is a scatterplot of data collected from 45 cities around the world in 1991. The horizontal axis represents the average number of work hours in a year, and the vertical axis represents the average teacher's salary in that city.
1. In words, describe the relationship between average work hours and teacher's salary.
2. Here are some summary statistics for these variables:
Data set = Mac, Summary Statistics
Variable N Average Std. Dev Minimum Median Maximum
WorkHrs 45 1883. 175.05 1583. 1856. 2375.
TeachSal 45 19.929 14.748 0.7 21. 58.
Data set = Mac, Sample Correlations
WorkHrs 1.0000 -0.3722
TeachSal -0.3722 1.0000
WorkHr TeachS
The regression line is yhat = 78.9711 - 0.0313558x.
a) Graph this line on the scatterplot
b) Interpret this regression line. Tells us everything you can about what the line tells us about the relationship between work hours and teacher's salaries for these 45 cities.
1. The data show a downwards trend that is roughly linear. Cities in which the average number of work hours per month is high tend to have low average teachers' salaries.
(Incidentally, in case you're thinking of moving, the cities with the two highest teachers' salaries and the relatively lower number of working hours are Geneva and Zurich. )
2. See the graph for the regression line.
2b) The regression line confirms our initial impression that the two variables are negatively associated. The slope is a negative value, and can be interpreted as meaning that cities in which the average monthly work hours are 1 hour greater, have an average teachers' salary that, on average, is about .03 thousands of dollars (or about $30) lower.
The relatively low correlation coefficient indicates that this regression line does not have great preditive ability. If you tell me the average working hours in a city, the regression line will only be able to give you a rough estimate of the average teachers' salary in that city. (However, as we'll see later, it's a good estimate of the average of all cities' average teachers salaries at that value of x.)