Further Analysis of Data - Using Statistical Inference and Regression Analysis
Part 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 tests and a level of confidence for any confidence intervals. 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.
Problem 1 - Topic 5
Your relative is considering buying a unit which from your previous research you have shown appears to be cheaper than houses. However, your relative is concerned that if they only consider units their choice will be limited.
To explore if their choice will be limited if they restrict their search to units use Type (4th column of your data) for all 100 residential properties for sale and an appropriate statistical inference technique to:
- Estimate the population proportion of residential properties for sale, in the location and state specified by your sample, which are units.
Hint: Sort data on Type to enable you to easily count the number of properties in your sample which are units
Problem 2 - Topic 6
Your relative has a maximum of $330,000 to purchase a residential property. If the average price of two or three bedroom residential properties is more than this your relative will consider the location to be too expensive.
Explore if your relative will find the location specified by your sample too expensive by using Price $000 (1st column of data) for two and three bedroom residential properties for sale, your output from Part A, and an appropriate statistical inference technique to answer the following question
- In the location specified by your sample, is the mean two and three bedroom residential property price more than $330,000?
Notes:
- The required data for two and three bedroom residential properties are in the first rows of your sample
- If you have sorted your data on Type in Problem 1 download your data again.
Problem 3 Topic 7
From your previous research you have shown that units appear to be cheaper than houses. Your relative asks you to estimate how much they would save if they purchased a unit instead of a house.
To provide a justified answer use Price $000 (1st column of data) and Type (4th column of data) for all 100 properties for sale, your output from Part A and an appropriate statistical inference technique to answer the following question.
- Estimate the mean difference in price between units and houses for sale in the location specified by your sample.
Hint: Sort data on Type to obtain two samples. One for house prices and the other for unit prices.
Problems 4 and 5 Simple and Multiple Linear Regression
Your relative asks what factors influence the price of a residential property and if you can estimate the price of a residential property from these factors.
To answer this you develop a simple linear regression model to estimate price from number of bedrooms and a multiple linear regression model to estimate price from number of bedrooms, number of bathrooms and type. Then you choose and interpret the linear model that best fits your data.
Problem 4 Simple Linear Regression Model Topic 8
Use Number of Bedrooms (2ndcolumn of data) as the independent variable and Price $000 (1st column of data) as the dependent variable for all 100 properties 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.
Problem 5 Multiple Linear Regression Model Topic 9
To explore whether being a house or unit and number of bathrooms also influences price, add Number of Bathrooms (3rd column of data) and Type (4th column of data) as additional independent variables to the simple linear regression model in Problem 4. Then develop and explore the relationship between price and the three independent 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 price by:
- Using appropriate tests to determine which independent variables make a significant contribution to the regression model.
- Then state or calculate the simple or multiple regression equation which best fits the data.
Part 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 relative.
Use the instructions given on page 4 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 Problem and put it in context
- Answer each Problem 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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Attachment:- Statistical Inference and Regression Analysis.zip