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.
Which variable should be the independent variable and which should be the dependent variable? Explain your answer in one or two complete sentences.
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
Which variable should be the dependent variable and which should be the independent
variable? Why?
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.
Analyze the data
Enter your data into your calculator or computer.
Write the linear equation below, rounding to 4 decimal places.
Calculate the following:
$a$ =
$b$ =
correlation =
$n$ =
equation:
$\hat{y}$ =
Obtain the graph of the regression line on your calculator. Sketch the regression line on the
same axes as your scatterplot.
Discussion questions
Is the correlation significant? Explain how you determined this in complete sentences.
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.
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?
For a car that weighs 4000 pounds, predict its fuel efficiency. Include units.
Can we predict the fuel efficiency of a car that weighs 10000 pounds using the least
squares line? Explain why or why not.
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?
Are there any outliers? If so, which point is an outlier?
** This lab was designed and contributed by Diane Mathios.
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
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
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?
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.