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Questions says that we have to show the workings in the spreadsheet which i have attached and the word limit is not a must to be 2000

ASSIGNMENT: MODELLING ESTABLISHED HOUSE (RESALE) PRICES FOR MELBOURNE

Housing affordability is a major issue in Australia these days. House prices in Melbourne has soared in the last 5 years. In this assignment you are asked to model established house (resale) prices in Melbourne.

To that end, you are presented with the housing.xsls data set. Your data set contains your dependent (or explained or Y) variable, Quarterly Established Median House Prices in Melbourne, from March 2002 to March 2014 (49 observations).

It also contains 6 other potential independent (or explanatory or X) variables. Namely (quarterly): Australian Real GDP (Percentage Change) (GDP); Exchange Rate (AUD/USD) (FX);

Inflation in Melbourne (CPI) (INF); Interest Rate (Cash Rate) (INT); Percentage Australian Population Change (POP); Real (National) Weekly Wages (in 100's Dollars) (WAGE). Listed here in alphabetical order.

Your task is to use the relevant independent variables to explain your dependent variable house prices. In order to model house prices (which you may call HP) answer the questions below and complete your assignment.

PART A: UNDERSTANDING THE DATA

1. For your dependent variable (housing prices), compute the following and provide a brief interpretation of:
a. Mean
b. Median
c. Standard Deviation
d. Skewness
e. Kurtosis

2. If we assume that house prices were actually normally distributed and assuming the mean and standard deviation you calculated in (1) is a good approximation of the population mean and population standard deviation;

a. What would the probability be that a given house selected at random would have a house price above $700,000?

b. What would the probability be that a group of 20 houses would have an average house price less than $500,000? (Hint: think about this one a little bit, it's more obvious than you think)

3. You believe house prices may have some outliers. In the presence of outliers, would the mean or median be the better measures of central tendencies? Briefly justify your answer.

PART B: SIMPLE LINEAR REGRESSION ANALYSIS

In this section you will be invited to build a simple linear regression model.

1. Under ideal conditions, Ordinary Least Squares (OLS) is said to be a preferred choice of estimation/method as it is the best linear unbiased estimator (BLUE). What are these ideal conditions? List them in their mathematical notation form and briefly, in one or two lines, describe what they mean.

2. For the following simple regression models, briefly discuss your a priori expectations regarding the slope coefficient. Justify your answer using either economic theory, intuition, or examples via case studies.

i. HP = β₁ +  β₂INT + e

ii. HP = β₁ +  β₂GDP + e

iii. HP = β₁ +  β₂FX + e

iv. HP = β₁ +  β₂POP + e

Note - In terms of the a priori expectations you should be stating what you expect the relationship between the dependent and explanatory variable to be like; i.e. positive, negative, or no relation.

3. For each of the simple regression models as per Part B - Qn (2) estimate each model separately using the Least Squares method and present your results in as an estimated simple regression function rather than in its tabular form.

4. Based on the above answer from Part B, interpret your estimated intercept and slope coefficients. During your interpretation, indicate whether the results meet you're a priori expectations. If not then discuss why you think it may differ.

PART B: SIMPLE LINEAR REGRESSION ANALYSIS

5. Based on the above models, carry out the following tests using a 1% and 5% level of significance.

a. Test whether Percentage Australian Population Change has a statistically positive and significant effect on house prices.

b. Test whether Interest Rate (Cash Rate) has a statistically negative and significant effect on house prices.

Note - As part of your hypothesis test you will need to indicate the Null and Alternative hypotheses, the test statistic itself along with how you would manually calculate it, the critical value, and your conclusion which relates back to the example.

PART C: MULTIVARIATE REGRESSION ANALYSIS

In this section you will be building on the simple regression analysis and doing a multivariate regression model.

1. Noting that your dependent variable is Median House Price, and your independent variables are: Australian Real GDP; Exchange Rate (AUD/USD); Inflation in Melbourne (CPI); interest rates (Cash Rate); Percentage Australian Population Change (Pop); and Real National Weekly Wages:

a. Add all the independent variables as per above to your model and specify the population regression function in its proper notational form.

b. Estimate the model and interpret the estimated coefficients (intercept/slope). It is sufficient to just show the regression output table.

2. After having done the estimation, we would like to verify the validity of our model and whether it sufficiently explains Median House Prices in Melbourne. To that end:

a. Test that the model is overall significant at the 5% level of significance. In your answer, state the null and alternative hypotheses, the test statistic and it's calculation, the critical value, and your conclusion.

b. What is the explanatory power of your model and how is it measured?

c. Compare your models from Part (B) to Part (C), which of these models would you prefer and why?

3. Adding extra independent variables on the surface might help improve our models fit, by pure reasoning then, we should keep adding more and more variables into the model. Why might this be a bad thing?

Attachment:- Data.xlsx