MAT10251 - Statistical Inference and Regression and Correlation - Simple Linear Regression - Multiple Linear Regression - Statistics Assignment Help

Assignment Task:

Task 1 - Appendices Statistical Inference and Regression and Correlation Tasks 

The following statistical tasks should appear as appendices to your written answers. These should include all 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 –

The theoretical maximum download speed on a 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 

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 

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?

Note: Difference Download Speed (8th column of data) may be used as an alternative to Speed Test 1 Download (4th column of data) and Speed Test 2 Download (6th column of data).

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 evening or not. Then you choose and interpret the linear model that best fits your data. 

Question 4 Simple Linear Regression Model 

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:

• Calculating the least squares regression line, correlation coefficient and coefficient of determination.

• Interpreting the gradient and vertical intercept of the simple linear regression equation.

• Interpreting the coefficient of determination.

Question 5 Multiple Linear Regression Model 

To explore whether being evening (7 pm to 11 pm) or not also influences upload speed add Evening (3rd column of data) as a second independent variable, to develop and then explore the relationship between the three variables by:

• Calculating the multiple regression equation and coefficient of determination.

• Interpreting the values of the multiple regression coefficients.

• 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:

• Using appropriate tests to determine which independent variables make a significant contribution to the regression model.

• 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 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:

• Introduce each question and put it in context

• Answer each question in non-statistical language.

• Present the result of your calculations and tests without unnecessary statistical jargon

• Include a conclusion which answers the given question. 

In particular, for Questions 4 and 5

• Include and justify the best model.

• Discuss and interpret the values of the regression coefficients and coefficient of determination of the best model.

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