|Course title and code||Mathematical Applications, Course Code 1137(Tertiary)|
|Semester unit title, codes and value||Unit 3 Mathematical Applications, Unit Code 11306|
1.0 for Semester Unit
|Assessment item type||Assignment|
|Marked out of||A synthetic score will be generated from z-scores|
Year 12 Mathematical Applications assignment
Your assignment is on bivariate data analysis. You will do two investigations into the relationships of two different pairs of numerical variables, the first using a two-way table and the second using your knowledge of linear regression. You will choose the two pairs of numerical variables. You will demonstrate your knowledge of the mathematical ways of examining data and present your findings. The assignment is in three parts, your data selection, a two-way table analysis and a scatter plot analysis.
You are expected to include all graphs and table in one Word document after creating them in Excel or Google sheets.
You will find the data for your scatter plot analysis and submit it to your classroom teacher. This is to ensure that you are on the right track and have suitable data that is in the right form for you to begin your analysis. This is due Thursday of week 13 by 10 pm.
Your submission should be a google sheet or excel spreadsheet with your data in table form. You should have two sets of data that you are going to compare.
Part 2 - 30%
You will select two questions from the questionnaire and use a two-way table to explore the relationship between them. Note that there may be no relationship—this is fine. You will need to discuss what about the data made you conclude that there was no relationship. Then you must discuss your data and what the tables show you about the data. You should write 200 words on this, including answering questions about the data that you pose yourself—for example, ‘What percentage of people who like A dislike B?’
For this part of the assignment, you must also include the following clearly labelled tables:
1.) The numerical two-way table;
2.) Percentage two-way tables by rows and by columns;
3.) The total percentage two-way table.
Part 3 - 70%
For this part of the assignment, you need to find two pairs of numerical variables to form the basis of your investigation.
Here is a short list of some possible examples of pairs of numerical variables that you could investigate:
•height and intelligence;
•temperature and rainfall for a particular location or region;
•latitude and skin cancer deaths;
•BMI (body mass index) and time in surgery;
•heights of husbands and heights of wives at marriage;
•wealth and happiness;
•years married and life expectancy;
•GDP (gross domestic product) per capita and life expectancy;
Note that these are only suggestions—the possibilities are immense.
Part 2 Answer
For this purpose, two questions selected are:
The numerical two-way table is as follows:
|COUNT||Do you play cricket?||Do you own a bicycle?||TOTALS|
It can be seen that out of a sample set of 160, 8 play cricket while remaining 152 do not play cricket. It can be seen that out of a sample set of 160, 112 own a bicycle while remaining 48 do not own a bicycle.
Hence, overall there are 120 positive responses and 200 negative responses.
It was also seen that out of 8 who play cricket, 7 also own bicycle. While out of 152 those who don’t play cricket, 105 own bicycle. Hence, it seems there is no relation between two variables and bicycle is more popular than playing cricket.
Percentage two-way tables by rows and by columns and the total percentage two-way table are as follows:
|PERCENTAGES||Do you play cricket?||Do you own a bicycle?||TOTALS|
Instead of numerical count, the above table presents same data in form of percentages which is easier to compare across categories, especially when the sample size is different. We can see that only 5% of respondents play cricket with an overwhelming 95% not playing cricket. The response is very different when it comes to owning bicycles. As many as 70% of the respondents own bicycle with only 30% who do not own a bicycle.
Due to majority negative responses for cricket question, the overall negative responses account for 62.5% with only 37.5% positive responses.
Part 3 Answer
Using data provided by WorldBank, Australian GDP and lending interest rate data have been taken for 40 years ranging from 1979 till 2018:
|GDP (current US$)||GDP (current US$ bn)||Lending interest rate (%)|
The hypothesis is to test whether there is a negative relationship between the GDP and lending interest rate. In other words, as GDP increases, lending rate decreases and vice versa.
Scatter plot is as follows:
Regression was done using excel:
The R is 0.66 which indicates reasonable positive relationship between the variables as r ranges from -1 to 1. P-value is less than significance value of 0.05 indicating that the model and coefficients are statistically significant. The regression equation is y = 1,489.75 - 94.6x where y is predicted GDP in USDbn and x is the lending interest rate.
The residuals data and plot are:
|Observation||Predicted GDP (current US$ bn)||Residuals||Standard Residuals|
The above residual plot indicates a definite pattern where residuals move up and down in a wave like pattern. Hence, the residuals may indicate that the regression model may not be linear but a second order model.
From above scatter plot and regression, we can conclude that there is definitely a relationship between GDP and lending interest rates in Australia. However, the relationship is positive and also regression equation that should be used is most probably of second order rather than linear as indicated by residual plot.