**Assignment Task**

Belle would like to know if the sample data is statistically different to what the media is suggesting. Remember to state your assumptions and limitations of the result.

In addition to this, Belle would like better understand if housing cost is a problem amongst low income earners i.e. household that earn less than $60,000 and older individuals. To begin, Belle would like you to run a simple linear regressions with:

hcost as the dependent variable; and age as the independent variable.

As part of your reporting, you need to interpret the coefficients of the model and discuss whether they are economically and statistically significant. Also report the confidence interval of dependent variable and interpret the results.

Next, Belle wants you to run a multiple linear regression. As part of this exercise you need to:

Explain why a multiple linear regression is beneficial i.e. justify the need for multiple linear regression and the issues associated with running a simple linear regression. Contextualise it in the context of the current problems are there confounding factors which motivate you to do this?

Associated with this think about the what type of model you’d like to use e.g. level-level, log-level, log-log or level-log model for each of the considered variables. You need to justify this.

Run the model with the following independent variables:

Ptypelocation

Internal size;Carspace;Marital status;age; and hcost as the dependent variable. You should also construct at least one interaction variables but it must make sense and must be justified. Creativity will be rewarded if you do this and you (i) construct it correctly, (ii) justify it and (iii) provide an interpretation of this variable.

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Get Help Now!As part of the reporting requirements for the multiple linear regression:

Interpret the coefficients.

Define and comment whether each of the coefficients are statistically significant. Remember to state your assumptions.

Define and comment whether each of the coefficients are economically significant. Remember to state your assumptions. You’ll also need to define what is economically significant and use a benchmark to determine this.

Limitations and issues with your model. If you decide to use technical terms e.g. multicollinearity, homoskedasticity, bias, consistency etc. you need to explain what these terminologies are and place them in the context of your problem and how it will affect your results.

The question which you need to help the government answer is (1) whether low income earners do face more financial stress and (2) whether older people face more financial stress.

Common reporting mistakes made by students (avoid these ????)

Regarding the simple linear regression, many of your peers struggled with the construction of the confidence interval of price (dependent variable). Associated with this is a struggle to interpret what I actually means. Please refer to the lecture notes below for further insights into this.

A lot of students tend to treat this as simply as another variable and construct a confidence interval around it this is not what we are looking for, we’re looking at the confidence interval given some value of the independent variable.

Regarding multiple linear regression. The common mistakes of made by your peers in the past is the lack of justification of the functional form and the reason why a multiple linear regression model is needed. Remember the ability to control for other factors is one thing but it is very important for you to contextualise it in the context of your problem.

In the same vein, many of your peers in the past really did not justify why they used a pure level-level model. Think about what a linear model means, do you expect the relationship to be linear. You should construct an interaction variable; you will need to justify it (often missed by the student) and interpret it (often misinterpreted). In fact, many students tended to also mis-interpret the marginal impacts given the presence of the interaction variables. Please be careful here. Have a look at the following slides:

Interpretation is also a common issue especially when it comes to log models. Your peers in the past have got this confused. So please pay attention to this. Finally, a very common mistake was the discussion of economic significance. Often your peers says it is without much justification, you’ll need a benchmark to make your case more compelling e.g. using the average of that variable as a benchmark may be a good starting point but we also know what the issues are with averages. Another common mistake is that students often forget what statistical significance means, it means that it is not zero, and often do not state this nor do they recognize its implications. Remember that you can also perform other tests beyond testing it as zero.

I urge you to please take note of all of this when you are writing up your report. If this is still unfamiliar you should immediately see your tutor or lecturer.

Commonly missed point made by students (consider these ????)

The commonly missed points have often been the lack of acknowledgement of limitations for all aspects i.e. chi-squared test, simple linear regression and multiple linear regression. For example when we talk about the chi-squared test, there is a lack of acknowledgement that samples are subject to errors and if you have a different sample you could conclude differently. This is just one. In this vein assumptions for the chi-squared test often gets neglected.

For simple linear regression, think about the problems of using a simple linear regression, you should try to use examples to highlight these problems. More often needs to be said for the limitations of a simple linear regression to provide a segue into why you would want to move to a multiple linear regression.

Another basic point is that many students have failed to answer the final question and sum up their findings. Many have focused so much on their analysis they forgot to answer the question of interest.

**Data**

Each student is assigned a personalized data set. Each individual data set refers to the problem above and has the same structure. However, values of some of the key variables will vary across students, meaning that statistical results and any inferences drawn from them may differ across students.

Each data set contains a sample of 293 observations, where each observation refers to a separate survey response. There are 11 variables, and they are as follows:

Variable Description

PTypeIndicator of the type of property sold:

1=Apartment

2=House

3=Townhouse

4=Villa

5=Other

location Location of the property bought

1 = Eastern suburbs

2= Northern suburbs

3 = Sydney CBD

4 = Western suburbs

5 = Southern suburbs

bedroom Number of bedroom(s) in the property

intsizeInternal size of the property in square metres (Sqm)

pricesoldThe price at which the property was sold

TincomeTotal annual income of the household who purchased the property

marital status Indicator of the marital status of the buyer(s):

1=Single

2=Couple

3=Family (with children)

age (Average) age of the household purchaser(s) (in years)

carspaceNumber of carspace(s) for the property

hcost Housing cost-income ratios calculated as the ratio of weekly mortgage repayment(s) and weekly household income

bathroom Number of bathroom(s) in the property

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