MAT10251: Statistics Analysis Project - Preliminary Analysis - Appendices Statistical Inference and Regression - Statistics Assignment Help

Assignment Task:

Project Situation:

Your statistical analysis of internet speed data is to enable you to answer questions from a friend who has recently been connected to the NBN (National Broadband Network) on an NBN 50 plan. This plan gives a maximum download speed of 50 Mbps (megabits per second) and a maximum upload speed of 20 Mbps. Your friend is concerned that their download speed is not close to the given maximum.
Over the first month on the plan, your friend collected the given sample of download and upload speeds. Then as you are enrolled in a statistics unit has asked you to analyse it. To obtain the sample, your friend on 120 randomly selected occasions tested their upload and download speed using Speed Test 1. Then to check the accuracy of the speed test chosen tested their upload and download speed using a second speed test, Speed Test 2. In each part of the project, you are required to analyse the sample data in response to given questions and provide a written answer. Assume that each written answer is a part of a letter or email to your friend.

Tasks: Part A Submission:

Complete the following:

1) Download and save your data.

2) Download the Project Part A cover sheets, name and save this file as
   “Family Name_First Name_Part_A_Campus”

3) Enter your Sample Number on page 2 of the Part A coversheets.

4) Statistical Output:
For download and upload speeds in your sample perform the following  tasks:

a. Typical evening download speed:

Use Speed Test 1 Download (4th column of data) for evening speeds only to explore the typical evening download speed, by using Excel to:
1. Construct a frequency histogram or polygon for the evening download speed.
2. Calculate descriptive statistics for the evening download speed.

b. The difference in Download Speed:

Use Difference Download Speed (8th column of data) for all 120 observations to explore the accuracy of Speed Test 1, by using Excel to:
1. Construct a boxplot of the difference in download speeds 
2. Calculate descriptive statistics for the difference in download speeds

c. Relationship between download and upload speed:

Explore the relationship between download and upload speeds for Speed Test 1. 
Use Speed Test 1 Download (4th column of data) as the independent variable with Speed Test 1 Upload (5th column of data) as the dependent variable for all 120 observations in your sample to explore the relationship between download and upload speed by using Excel to:
1. Construct a scatter plot for download and upload speeds, Speed Test 1
2. Calculate the correlation coefficient for download and upload speeds, Speed Test 1.

5) Written Answer: Email or letter

Using the instructions given on pages 4 and 5 of the Part A coversheets, introduce your data and the results of your preliminary investigation of internet speeds.
This should be three to five pages and 400 to 800 words.
Use an appropriate style, without statistical jargon and equations, to clearly communicate your results.

6) Complete Coversheets 1 and 2, save and submit Part A of the project online using Project Part A link in Submit Project by the due date Tuesday 26 November 2019.

Task 1: Part B: Appendices Statistical Inference and Regression and Correlation Tasks:

The following statistical tasks should appear as appendices to your written answers. These should include all the necessary steps and appropriate Excel output. 
These appendices should come after your written answer within your single Word document for Part B.

Statistical Inference:
Choose a level of significance for any hypothesis test and a level of confidence for any confidence interval. Enter these values on page 2 of the Part B coversheets along with the sample number from Part A.
For your sample answer the following questions using appropriate statistical inference and regression techniques.

Question 1 – Topic 5:
The theoretical maximum download speed on an NBN 50 plan is 50 Mbps. Your friend asks you to estimate the proportion of time that they achieve at least 80%, that is, 40 Mbps or more, of this maximum.
To enable you to answer this use Speed Test 1 Download (4th column of your data) for all 120 observations and an appropriate statistical inference technique to:
Estimate the population proportion of time that the download speed is at least 40 Mbps. 

Question 2 – Topic 6:
Your friend asks on average does their evening download speed exceed the advertised typical evening download speed of 41 Mbps.
To provide a justified answer to the question use the evening download speed from Speed Test 1 Download (4th column of data), your output from Part A and an appropriate statistical inference technique to answer the following question
Is the mean evening download speed greater than 41 Mbps?

Question 3 – Topic 7:
To check the accuracy of the Speed Test 1 your friend repeated the test using a second speed test, Speed Test 2. On average each speed test should give the same download and upload speed.  
Your friend asks you to check if the two tests on average give the same download speed.
To provide a justified answer use Speed Test 1 Download (4th column of data) and Speed Test 2 Download (6th column of data) for all 120 observations in your sample, your output from Part A and an appropriate statistical inference technique to answer the following question.
Is there a difference in the average download speed given by the two tests?

Questions 4 and 5 – Simple and Multiple Linear Regression:
Your friend is interested in the relationship between download and upload speed. In particular, they ask you to estimate upload speed from download speed.
To do this you develop a simple linear regression model to estimate upload speed from download speed and a multiple linear regression model to estimate upload speed from download speed and whether it is an evening or not. Then you choose and interpret the linear model that best fits your data. 

Question 4 Simple Linear Regression Model Topic 8:
To explore the relationship between download and upload speed use Speed Test 1 Download (4th column of data) as the independent variable with Speed Test 1 Upload (5th column of data) as the dependent variable for all 120 observations in your sample and your output from Part A to develop and then explore a simple linear relationship between the two variables by:
1. Calculating the least-squares regression line, correlation coefficient and coefficient of determination.
2. Interpreting the gradient and vertical intercept of the simple linear regression equation.
3. Interpreting the coefficient of determination. 

Question 5 Multiple Linear Regression Model Topic 9:
To explore whether being evening (7 pm to 11 pm) or not also influences upload speed to add Evening (3rd column of data) as a second independent variable, to develop and then explore the relationship between the three variables by:
1. Calculating the multiple regression equation and coefficient of determination.
2. Interpreting the values of the multiple regression coefficients.
3. Interpreting the value of the coefficient of determination. Compare the value with the corresponding value for the simple linear regression model.

Then determine the best model to estimate upload speed by:
1. Using appropriate tests to determine which independent variables make a significant contribution to the regression model.
2. Then state the simple or multiple regression equation which best fits the data. 

Task 2 - Written Answer – Email or letter:

For Questions 1, 2, 3 and Questions 4 and 5 combined to present the results of your calculations, with your interpretation and conclusions as either a letter or email/emails to your friend.
Use the instructions given on pages 4 and 5 of the Part B coversheets.
This should be 400 to 900 words and two to five pages.
It should be submitted as a Word file with Excel output included.
 
Make sure you:
1. Introduce each question and put it in context
2. Answer each question in non-statistical language.
3. Present the result of your calculations and tests without unnecessary statistical jargon
4. Include a conclusion which answers the given question. 
5. In particular, for Questions 4 and 5
6. Include and justify the best model.
7. Discuss and interpret the values of the regression coefficients and coefficient of determination of the best model.

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