Call Now to Set Up Tutoring:

(888) 888-0446

HiSET: Math : Identify lines of best fit

Study concepts, example questions & explanations for HiSET: Math

Create An Account

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Data Analysis, Probability, And Statistics

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \\ 1 & 3.5 \\ 2 & 4.7\\ 3 & 6.0\\ 4 & 7.8 \end{matrix}$

Possible Answers:

y=1.42x+ 1.95

y= 0.6977x - 1.442

y = 0.6974x - 1.336

y = 1.433x + 2.067

y = 0.7692x- 1.615

Correct answer:

y=1.42x+ 1.95

Explanation:

The formula for a regression line for a set of paired data is the line of the equation

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

n = 4 , the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$b_{1} = \frac{4 (62.1)-(10)( 22.0)}{4(30)-(10)^{2}}$

$= \frac{248.4-220}{120-100}$

$= \frac{28.4}{20}$

=1.42

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{22}{4} = 5.5$

$b_{0} = \overline{y} - b_{1}\overline{x}$

$b_{0} =5.5 - 1.42 (2.5)$

=5.5 - 3.55

=1.95

The equation of the linear regression line is y=1.42x+ 1.95 .

Report an Error

Example Question #8 : Data Analysis, Probability, And Statistics

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \\ 1 &10.0 \\ 2 &8.7\\ 3 & 7.1 \\ 4 & 5.0 \end{matrix}$

Possible Answers:

y = -0.876x + 8.54

y = -1.66 x + 11.85

y= -0.5954x + 7.085

y = -0.625x + 7.438

y = -1.6x + 11.9

Correct answer:

y = -1.66 x + 11.85

Explanation:

The formula for a regression line for a set of paired data is the line of the equation

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

n = 4 , the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$b_{1} = \frac{4 (68.7)-(10)( 30.8)}{4(30)-(10)^{2}}$

$= \frac{274.8 - 308}{120-100 }$

$= \frac{-33.2}{20 }$

= -1.66

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{30.8}{4} = 7.7$

$b_{0} = \overline{y} - b_{1}\overline{x}$

=7.7 - (-1.66) (2.5 )

=7.7 +4.15

= 11.85

The linear regression line is the line of the equation y = -1.66 x + 11.85 .

Report an Error

View Tutors

Laurie
Certified Tutor

Monmouth College, Bachelor in Arts, English. National Louis University, Master of Arts Teaching, Special Education.

View Tutors

Ardo
Certified Tutor

Shanghai Jiao Tong University, Bachelor of Science, Mechanical Engineering.

View Tutors

Varun
Certified Tutor

University of Arizona, Bachelor of Science, Aerospace Engineering.

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Dallas Fort Worth, English Tutors in Seattle, MCAT Tutors in Phoenix, Chemistry Tutors in Denver, GMAT Tutors in Atlanta, Statistics Tutors in Atlanta, ISEE Tutors in San Francisco-Bay Area, LSAT Tutors in Washington DC, ISEE Tutors in Washington DC, Spanish Tutors in Philadelphia

Popular Courses & Classes

MCAT Courses & Classes in Boston, Spanish Courses & Classes in Washington DC, Spanish Courses & Classes in Seattle, Spanish Courses & Classes in Denver, GMAT Courses & Classes in Seattle, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego

Popular Test Prep

GMAT Test Prep in Boston, LSAT Test Prep in Chicago, SAT Test Prep in Boston, MCAT Test Prep in Miami, ACT Test Prep in Chicago, SSAT Test Prep in New York City, MCAT Test Prep in Washington DC, SSAT Test Prep in Chicago, GMAT Test Prep in Atlanta, GMAT Test Prep in Philadelphia

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HiSET: Math : Identify lines of best fit

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #7 : Data Analysis, Probability, And Statistics

Example Question #8 : Data Analysis, Probability, And Statistics

All HiSET: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: