Regression Analysis and Linear Models

SOUTHERN CROSS UNIVERSITY
School of Business and Tourism
MAT10251 Statistical Analysis
PROJECT COVER SHEET
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PART B
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MAT10251 – Statistical Analysis
Project Part B
Sample Number (last digit of your student ID
number)
5
Confidence Level 95%
Level of Significance 5%
Value: 25%
2

Marking and Feedback Sheet Part B
Cover sheet or sample incorrect
Format incorrect, including name
Statistical Tasks
Statistical Inference Question 1
Assumptions & other required steps
Calculation (Excel output)
Conclusion
Statistical Inference Question 2
Assumptions & other required steps
Calculation (Excel output)
Decision and onclusion
Statistical Inference Question 3
Assumptions & other required steps
Calculation (Excel output)
Decision and conclusion
Regression and Correlation
Assumptions and random variables defined
Simple Linear Model Question 4
Excel Output and Equation
Interpretation of regression coefficients & coefficient of determination
Multiple Linear Model Question 5
Excel Output and Equation
Interpretation of regression coefficients & coefficient of determination
Statistical Inference
Choice of technique and other required steps
Decision and conclusion
Best model
Total Statistical Tasks
Written Answer (Components of a report)
Question 1
Question 2
Question 3
Questions 4 & 5
Introduction and discussion of best model
Structure, grammar, spelling and revised Part A content
Total Report
Comments
3

Dear Friend,
To estimate the proportion of time for the population to have
download speed of at least 40 Mbps, that is, at least 80% of the maximum
speed, the confidence interval should be calculated. In this case, total
number of population data has to be considered, which is 120. It has been
observed that 17 observations in the download speed data have speed
more than 40 Mbps. Using these data, the confidence interval has been
calculated and the estimation of the population proportion of time ranges
from 8% to 21% for download speed of 40 Mbps (Refer to Appendix,
Answer 1).
Average evening download speed
The broadband service provider, NBN, puts up the advertisement
that the typical average download speed in the evening of their internet is
41 Mbps. To examine the claim of the company about their average
download speed, that is, whether it is more than 41 Mbps, one sample t-
test has been conducted. For the test, it is assumed that the average
download speed in the evening is 41 Mbps.
From the Descriptive Statistics, conducted in Part A, the average
download speed in the evening is found to be 24.5 Mbps, which is quite
less than the claimed speed of 41 Mbps. To conduct the one sample t-test,
first the download speed values for evening time have to be extracted.
With the application of Filter in MS Excel on the variables, ‘Evening’ and
‘Speed Test 1 Download’, only the speed values corresponding to the
Evening values are extracted. The one sample t-test has been performed
on the sorted data where variable 1 defines Speed Test 1 Download data
and variable 2 denotes the dummy variable as one sample t-test has to be
performed.
The outcome of the one sample t-test (Refer to Appendix, Answer 2)
provides the average of the download speed in evening as 24.5 Mbps and
this is equal to the average evening download speed value derived from
the descriptive statistics. The one-tail p-value is 0.00, which is less than
the critical alpha value of 0.05. This indicates that the null hypothesis
must be rejected, and the alternate hypothesis must be accepted. In other
words, the average download speed in the evening is less than the
promoted speed of 41 Mbps.
Checking the accuracy of Speed Test 1 Download
As it is necessary to check the accuracy of the first set of download
speed data, a second speed test was conducted and the values are
compared by applying independent sample t-test assuming unequal
variances. It has been assumed that both the download speed tests, that
is, Speed Test 1 Download and Speed Test 2 Download would generate
the same speed for download. Independent sample t-test has been
4