Sheet1 CarMPGWeightCylindersHorsepowerCountry Buick Skylark28.42670490U.S. Dodge Omni30.92230475U.S. Mercury Zephyr20.83070685U.S. Fiat Strada37.32130469Italy Peugeot 694...

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Sheet1
    Car    MPG    Weight    Cylinders    Horsepower    Country
    Buick Skylark    28.4    2670    4    90    U.S.
    Dodge Omni    30.9    2230    4    75    U.S.
    Mercury Zephyr    20.8    3070    6    85    U.S.
    Fiat Strada    37.3    2130    4    69    Italy
    Peugeot 694 SL    17.8    3410    6    133    France
    VW Ra
it    31.9    1925    4    71    Germany
    Plymouth Horizon    34.2    2200    4    70    U.S.
    Mazda GLC    34.1    1975    4    65    Japan
    Buick Estate Wagon    16.9    4360    8    155    U.S.
    Audi 5000    22.5    2830    5    103    Germany
    Chevy Malibu Wagon    19.2    3605    8    125    U.S.
    Dodge Aspen    18.6    3620    6    110    U.S.
    VW Dasher    30.5    2190    4    78    Germany
    Ford Mustang 4    26.5    2585    4    88    U.S.
    Dodge Colt    35.1    1915    4    80    Japan
    Datsun 810    22    2815    6    97    Japan
    VW Scirocco    31.5    1990    4    71    Germany
    Chevy Citation    28.8    2595    6    115    U.S.
    Olds Omega    26.8    2700    6    115    U.S.
    Chrysler LeBaron Wagon    18.5    3940    8    150    U.S.
    Datsun 510    27.2    2300    4    97    Japan
    AMC Concord D/L    18.1    3410    6    120    U.S.
    Buick Century Special    20.6    3380    6    105    U.S.
    Saab 99 GLE    21.6    2795    4    115    Sweden
    Datsun 210    31.8    2020    4    65    Japan
    Ford LTD    17.6    3725    8    129    U.S.
    Volvo 240 GL    19    3140    6    125    Sweden
    Dodge St Regis    18.2    3830    8    135    U.S.
    Toyota Corona    27.5    2560    4    95    Japan
    Chevette    30    2155    4    68    U.S.
    Ford Mustang Ghia    21.9    2910    6    109    U.S.
    AMC Spirit    27.4    2670    4    80    U.S.
    Ford Country Squire Wagon    28    4054    8    142    U.S.
    BMW 320i    23.1    2600    4    110    Germany
    Pontiac Phoenix    33.5    2556    4    90    U.S.
    Honda Accord LX    29.5    2135    4    68    Japan
    Mercury Grand Marquis    16.5    3955    8    138    U.S.
    Chevy Caprice Classic    17    3840    8    130    U.S.

Engineering Department, UMass Boston XXXXXXXXXXSpring 2022

ENGIN 322: Probability and Random Processes

Project #2: Sampling Theory and Linear Regression
Project Description
In this project, you will assume the part of an automotive manufacturer. In part I, you will provide
ackground analysis for the development of a new vehicle. In part II, you will develop a method for
sampling manufactured parts in order to determine the likelihood of failure. (Note: Data for Part I of the
project is slightly modified from: https:
www.statcrunch.com/5.0/viewresult.php?resid=1878105).
Part I
The spreadsheet ‘Vehicle_Info.xlsx’ provides detailed information about vehicles on the market. In Part I,
you should load the data into Matlab and compare vehicle properties to average miles per gallon (mpg).
a) Load the data set into Matlab with the readtable() function
) Determine the data set co
elation (i.e., Pearson’s r) for average mpg versus weight, number of
cylinders, and horsepower.
c) Use the scatter() and polyfit() functions to display the data points and linear regression curves
for average mpg versus weight, number of cylinders, and horsepower. For each of the 3 plots,
show average mpg on your Y axis. Label the resulting plots and include them in your report.
Question 1: Would you say that a vehicles horsepower impacts the average mpg? What about the impact
of weight and number and cylinders on average mpg? Explain your reasoning.
Question 2: Your company’s newest vehicle model will be a 6 cylinder that weighs 3,250lbs and has 100
horsepower. If your goal is to be above the regression line for every category, what average mpg should
you strive for?
Part II
Assume that you have received reports of faulty headlights. The data values in the file
‘population_data.mat’ represent the population of headlights on the production line (0 represents a good
headlight, 1 represents a faulty headlight). You are unable to test all headlights; but you are able to
andomly sample ?? of the headlights as they come off the production line. In Part II, you should simulate
the following in Matlab for values of ?? ranging from 1 to 2000.
a) For each value of ??, randomly sample n headlights from the population and determine the sample
mean and sample variance (i.e., the percentage of faulty headlights in your sample and the
associated variance of the sample).
) Plot the sample mean and sample variance versus the sample size.
Question 1: What do you notice about the sample mean and sample variance as you increase sample size?
Question 2: Based on your plots, what can you predict about the percentage of headlights in the
population that are faulty? Explain your reasoning. (Hint: Zoom in on the values from n=1000 to n=2000
for a better visualization. You can compare your prediction to the true mean by determining the mean
value of the full set of values from ‘population_data.mat’)
https:
www.statcrunch.com/5.0/viewresult.php?resid=1878105
Grading Metrics
• Coding and Results: 30%
• Theoretical Analysis: 40%
• Written Report: 30%
Coding and Results: This portion of the project will be graded based on the implementation of code as
described for Part I and II above. Results should include a description of the observed outcomes and some
depiction of the results from your code.
Theoretical Analysis: This portion of the project will be graded based on your answers to the questions
above. Be sure to clearly indicate the answers AND REASONING for each of the questions within your
written report.
Written Report: The written report should be submitted on blackboard by midnight on April 8. The report
should be 3-5 pages including an overview of the project, expected outcomes, your analysis method,
esults, and observations. You may include any code as an appendix.
    Project Description
    Part I
    Part II
    Grading Metrics
    Part II - Old
Answered 2 days AfterApr 05, 2022

Solution

Vishvajeet answered on Apr 07 2022
17 Votes
Engineering Department, UMass Boston Spring 2022
ENGIN 322: Probability and Random Processes
Project #2: Sampling Theory and Linear Regression
Name:……………………………………………… ID:………………………..
Name:……………………………………………… ID:……………………….
Table of Contents
Title Page
1
Objective
3
Introduction
3
Apparatus
3
Procedure
3
Results and Discussion
4-11
Conclusion
References
11
11
Objective: In this project, you will assume the part of an automotive manufacturer. In part I,
you will provide background analysis for the development of a new vehicle. In part II, you will
develop a method for sampling manufactured parts in order to determine the likelihood of
failure.
Introduction:
Regression analysis is an important statistical method for the analysis of data. By applying
egression analysis, we are able to examine the relationship between a dependent variable and
one or more independent variables. In this article, I am going to introduce the most common
form of regression analysis, which is the linear regression. As the name suggests, this type of
egression is a linear approach to modeling the relationship between the variables of interest.
Method
Linear regression is used to study the linear relationship between a dependent variable (y) and
one or more independent variables (X). The linearity of the relationship between the
dependent and independent variables is an assumption of the model. The relationship is modeled
through a random distu
ance term (or, e
or variable) ε. The distu
ance is primarily
important because we are not able to capture every possible influential factor on the dependent
variable of the model. To capture all the other factors, not included as independent variable, that
affect the dependent variable, the distu
ance term is added to the linear regression model.
In this way, the linear regression model takes the following form:
where
are the regression coefficients of the model (which we want to estimate!), and K is the number
of independent variables included. The equation is called the regression equation.
Simple linear regression
Let’s take a step back for now. Instead of including multiple independent variables, we start
considering the simple linear regression, which includes only one independent variable. Here,
we start modeling the dependent variable yi with one independent variable xi:
where the subscript i refers to a particular observation (there are n data points in total). Here, β0
and β1 are the coefficients (or parameters) that need to be estimated from the data. β0 is the
intercept (a constant term) and β1 is the gradient.
In simple linear regression, we essentially predict the value of the dependent variable yi using
the score of the independent variable xi, for observation i.
Apparatus/Tools:
• Personal Computer or Laptop.
• MATLAB etc
Procedure:
Results and Discussion:
Part 1 –
a) Load the data set into Matlab with the readtable() function
) Determine the data set co
elation (i.e., Pearson’s r) for average mpg versus weight, number
of cylinders, and horsepower.
c) Use the scatter() and polyfit() functions to display the data points and linear regression curves
for average mpg versus weight, number of cylinders, and horsepower. For each of the 3 plots,
show average mpg on your Y axis. Label the resulting plots and include them in your report.
Part 2 –
Assume that you have received reports of faulty headlights. The data values in the file...
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