## MAT 351 Mathematical Modelling Scatter Diagrams & Correlations Worksheet

MAT 351 Mathematical Modelling Scatter Diagrams & Correlations Worksheet

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Hi,

I need step-by-step solutions to all the 5 questions in the attached file. The questions are related to linear/exponential curve fitting. Please follow all the instructions given in the document.

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**MAT-351: MATHEMATICAL MODELING**

Midterm Project

# OVERVIEW

You are required to complete a midterm project that addresses modeling problems. The project will focus on the topics covered in the first three modules of the course from Chapter 1 to 7 of the textbook.

*Course objectives covered in this project include CO1, CO2, CO3, CO4, CO5, CO6, CO7, CO8, CO10*

# PROJECT DETAILS AND REQUIREMENTS

- Given the data in the table below construct a scatter diagram.

x | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

y | 5450 | 6376 | 3730 | 3525 | 3062 | 1063 | 1880 | 1401 | 1231 | 490 |

x | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 |

y | 1067 | 1053 | 664 | 246 | 353 | 412 | 150 | 68 |

- For the data in Question 1, is the coefficient of correlation positive, negative, or zero? Fit a line by eye through the points of the scatter diagram that was constructed in Question 1. Fit a line through the data using the least squares technique.

- The data in the above table is the daily count of COVID-19 cases in New York City every 5 days starting April 1 to June 26, 2020. Is the linear model in Question 2 the best fit? If yes, explain why. If not, give the equation of a better model and explain your rationale.

- Given the parabola y = 2x
^{2}+ 3, let x take on the values 1, 2, 3, 4, 5, 6, and 7. Find the corresponding y values. Which type of function (logarithmic or exponential) will best fit the given parabola?

- Fit the data in Question 4 to either a logarithmic or exponential curve depending on your choice from Question 4.

**Note: **It is recommended you use Desmos, a free online graphing utility to create graphs and diagrams for the midterm project. To generate a graph, click on **Math Tools** at the top and select **Graphing Calculator** from the dropdown menu. Click on the menu bars to the left of **Untitled Graph** in the top left-hand corner, and choose your intended kind of graph from the dropdown menu.

# WRITING AND RESEARCH RESOURCES

The following links provide online writing and research aids to help you with your paper assignments.

- OWL (Online Writing Lab) at Purdue University
- Writer’s Handbook, the Writing Center at the University of Wisconsinâ€“Madison
- APA Guidelines
- Information Literacy for TESU Students (an online guide from the New Jersey State Library to assist you in starting your research, searching databases for articles, citing sources, using ILLiad to request books or articles, etc.)

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