Skip to content Skip to navigation

Connexions

You are here: Home » Content » Linear Regression and Correlation: Practice

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCOT Project display tagshide tags

    This module is included in aLens by: CC Open Textbook ProjectAs a part of collection:"Collaborative Statistics"

    Click the "CCOT Project" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection:"Collaborative Statistics"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection:"Collaborative Statistics"

    Comments:

    "Collaborative Statistics was written by two faculty members at De Anza College in Cupertino, California. This book is intended for introductory statistics courses being taken by students at two- […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lucy Van Pelt display tagshide tags

    This module is included inLens: Lucy's Lens
    By: Tahiya MaromeAs a part of collection:"Collaborative Statistics"

    Comments:

    "Part of the Books featured on Community College Open Textbook Project"

    Click the "Lucy Van Pelt" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

  • Educational Technology Lens display tagshide tags

    This module is included inLens: Educational Technology
    By: Steve WilhiteAs a part of collection:"Collaborative Statistics"

    Click the "Educational Technology Lens" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

  • SHN CNX Workshop display tagshide tags

    This module is included inLens: Stategic Horizon Network Workshop on Alternative Couseware -- Connexions Session
    By: ConnexionsAs a part of collection:"Collaborative Statistics"

    Comments:

    "This textbook is used in many sections of community college statistics around the country. The PDF version of the book is also available in the Florida Orange Grove repository."

    Click the "SHN CNX Workshop" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

  • Bio 502 at CSUDH display tagshide tags

    This module is included inLens: Bio 502
    By: Terrence McGlynnAs a part of collection:"Collaborative Statistics"

    Comments:

    "This is the course textbook for Biology 502 at CSU Dominguez Hills"

    Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Linear Regression and Correlation: Practice

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

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

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Student Learning Outcomes

  • The student will explore the properties of linear regression.

Given

The data below are real. Keep in mind that these are only reported figures. (Source: Centers for Disease Control and Prevention, National Center for HIV, STD, and TB Prevention, October 24, 2003)

Table 1: 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

Note:

We will use the columns “year” and “# AIDS cases diagnosed” for all questions unless otherwise stated.

Graphing

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.

Data

Exercise 1

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

Linear Equation

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

Exercise 2

Calculate the following:

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

Solution

  • a. a = -3,448,225 a = -3,448,225 size 12{a="-3,448,225"} {}
  • b. b = 1750 b = 1750 size 12{b="1750"} {}
  • c. corr . = 0 . 4526 corr . = 0 . 4526 size 12{ ital "corr" "." =0 "." "4526"} {}
  • d. n = 22 n = 22 size 12{n="22"} {}

Exercise 3

equation: y^=y^= size 12{ { hat {y}}={}} {}

Solution

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

Solve

Exercise 4

Solve.

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

Solution

  • a. 25082
  • b. 33,831

Plot

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.

Exercise 5

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

Exercise 6

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

Exercise 7

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

Exercise 8

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

Exercise 9

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

Exercise 10

Solve.

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

Solution

  • a. -1164

Content actions

Give Feedback:

E-mail the module authors | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks