Notes on integration and measure
P. B. Kronheimer, for Math 114
Revised, September 12, 2010
These are some outline notes on integration and measure, based on the book by Stein and Sharkarchi
that we are using in class, but adapted to the approach we will
We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares
equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the
explanatory or predictor variable is displayed.
Let x be the number of different research programs, and let y be the mean number of patents per
program. As in any business, a company can spread itself too thin. For example, too many research
programs might lead to a decline in overall research producti
An economist is studying the job market in Denver area neighborhoods. Let x represent the total
number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same
neighborhood. A sample of six Denver neighborhoods gave
How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y
be the average weight of the pony (in kilograms).
x 3 6 12 16 21
y 60 95 140 160 175
(a) Use a calculator to verify that x = 58, x2 = 886, y = 63
Examine the computation formula for r, the sample correlation coefficient.
(a) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get
the same (equivalent) result? Explain your answer.
The result is the same be
The initial visual impact of a scatter diagram depends on the scales used on the x and y axes. Consider
the following data.
x 1 2 3 4 5 6
y 1 4 6 3 6 7
(a) Make a scatter diagram using the same scale on both the x and y axes (i.e., make sure the unit
Asian economies impact some of the world's largest populations. The growth of an economy has a big
influence on the everyday lives of ordinary people. Are Asian economies changing? A random sample
of 15 Asian economies gave the following information about
The correlation coefficient r is a sample statistic. What does it tell us about the value of the population
correlation coefficient (Greek letter rho)? You do not know how to build the formal structure of
hypothesis tests of yet. However, there is a quick