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

Class Time:

Names:

Student learning outcomes:

  • The student will calculate and construct the line of best fit between two variables.
  • The student will evaluate the relationship between two variables to determine if that relationship is significant.

Collect the data

Use the most recent April issue of Consumer Reports. It will give the total fuel efficiency (in miles per gallon) and weight (in pounds) of new model cars with automatic transmissions. Wewill use this data to determine the relationship, if any, between the fuel efficiency of a car and its weight.

  1. Which variable should be the independent variable and which should be the dependent variable? Explain your answer in one or two complete sentences.
  2. Using your random number generator, randomly select 20 cars from the list and record their weights and fuel efficiency into the table below.
    Weight Fuel Efficiency
  3. Which variable should be the dependent variable and which should be the independent variable? Why?
  4. By hand, do a scatterplot of “weight” vs. “fuel efficiency”. Plot the points on graph paper. Label both axes with words. Scale both axes accurately.
    Blank graph with vertical and horizontal axes.

Analyze the data

Enter your data into your calculator or computer. Write the linear equation below, rounding to 4 decimal places.

  1. Calculate the following:
    • a =
    • b =
    • correlation =
    • n =
    • equation: y ^ =
  2. Obtain the graph of the regression line on your calculator. Sketch the regression line on the same axes as your scatterplot.

Discussion questions

  1. Is the correlation significant? Explain how you determined this in complete sentences.
  2. Is the relationship a positive one or a negative one? Explain how you can tell and what this means in terms of weight and fuel efficiency.
  3. In one or two complete sentences, what is the practical interpretation of the slope of the least squares line in terms of fuel efficiency and weight?
  4. For a car that weighs 4000 pounds, predict its fuel efficiency. Include units.
  5. Can we predict the fuel efficiency of a car that weighs 10000 pounds using the least squares line? Explain why or why not.
  6. Questions. Answer each in 1 to 3 complete sentences.
    • Does the line seem to fit the data? Why or why not?
    • What does the correlation imply about the relationship between fuel efficiency and weight of a car? Is this what you expected?
  7. Are there any outliers? If so, which point is an outlier?

** This lab was designed and contributed by Diane Mathios.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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