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This module provides a practice of Linear Regression and Correlation as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student learning outcomes

  • The student will evaluate bivariate data and determine if a line is an appropriate fit to the data.


Below are real data for the first two decades of AIDS reporting. ( Source: Centers for Disease Control and Prevention, National Center for HIV, STD, and TB Prevention )

Adults and adolescents only, united states
Year # AIDS cases diagnosed # AIDS deaths
Pre-1981 91 29
1981 319 121
1982 1,170 453
1983 3,076 1,482
1984 6,240 3,466
1985 11,776 6,878
1986 19,032 11,987
1987 28,564 16,162
1988 35,447 20,868
1989 42,674 27,591
1990 48,634 31,335
1991 59,660 36,560
1992 78,530 41,055
1993 78,834 44,730
1994 71,874 49,095
1995 68,505 49,456
1996 59,347 38,510
1997 47,149 20,736
1998 38,393 19,005
1999 25,174 18,454
2000 25,522 17,347
2001 25,643 17,402
2002 26,464 16,371
Total 802,118 489,093
We will use the columns “year” and “# AIDS cases diagnosed” for all questions unless otherwise stated.


Graph “year” vs. “# AIDS cases diagnosed.” Plot the points on the graph located below in the section titled "Plot" . Do not include pre-1981. Label both axes with words. Scale both axes.


Enter your data into your calculator or computer. The pre-1981 data should not be included. Why is that so?

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Linear equation

Write the linear equation below, rounding to 4 decimal places:

For any prediction questions, the answers are calculated using the least squares (best fit) line equation cited in the solution.

Calculate the following:

  • a = size 12{a={}} {}
  • b = size 12{b={}} {}
  • corr . = size 12{ ital "corr" "." ={}} {}
  • n = size 12{n={}} {} (# of pairs)

  • a = -3,448,225 size 12{a="-3,448,225"} {}
  • b = 1750 size 12{b="1750"} {}
  • corr . = 0 . 4526 size 12{ ital "corr" "." =0 "." "4526"} {}
  • n = 22 size 12{n="22"} {}
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equation: y ^ = size 12{ { hat {y}}={}} {}

y ^ = -3,448,225 size 12{ { hat {y}}="-3,448,225"} {} + 1750 x size 12{+"1750"x} {}

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  • When x = 1985 size 12{x="1985"} {} , y ^ = size 12{ { hat {y}}={}} {}
  • When x = 1990 size 12{x="1990"} {} , y ^ = size 12{ { hat {y}}={}} {}

  • 25,525
  • 34,275
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Plot the 2 above points on the graph below. Then, connect the 2 points to form the regression line.

Blank graph with horizontal and vertical axes.

Obtain the graph on your calculator or computer.

Discussion questions

Look at the graph above.

Does the line seem to fit the data? Why or why not?

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Do you think a linear fit is best? Why or why not?

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Hand draw a smooth curve on the graph above that shows the flow of the data.

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What does the correlation imply about the relationship between time (years) and the number of diagnosed AIDS cases reported in the U.S.?

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Why is “year” the independent variable and “# AIDS cases diagnosed.” the dependent variable (instead of the reverse)?

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  • When x = 1970 size 12{x="1970"} {} , y ^ = size 12{ { hat {y}}={}} {} :
  • Why doesn’t this answer make sense?

  • -725
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Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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Damian Reply
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Introduction about quantum dots in nanotechnology
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s. Reply
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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