Data Set

In this assignment you will be using the data set provided in the Excel file named as "MAE256 Assignment Data Set.xlsx" which is uploaded to the Assignment folder under the Assessment Resources on CloudDeakin. This data sets contains information on 1000 house sales from a city in the USA. More specifically, the data set has the following six variables:

1. size: the number of square meters of the living area,

2. age: age of the house in years,

3. proximity: a dummy (binary) variable which takes the value of 1 if the house is near a major business district and the value of 0 otherwise,

4. pool: a dummy(binary) variable which takes the value of 1 if the house has a swimming pool and the value of 0 otherwise,

5. fireplace: a dummy(binary) variable which takes the value of 1 if the house has a fireplace and the value of 0 otherwise,

6. price: sale price in thousands of dollars.

QUESTIONS
Using Excel, compute and present the descriptive statistics of house sale prices. Provide a brief interpretation of mean, median, standard deviation and skewness.

Given your computations in Q.1. of the mean and standard deviation, find the proportion of houses with sale prices within one-standard deviation from the mean house price.

Plot the variable price against size and proximity in two separate scatter diagrams. Given your scatter diagrams, what do you observe about the relationship between house prices and size and proximity?

Now estimate a linear regression model of the following form:

price_i= β₀+ β₁size_i + β₂age_i + β₃proximity_i+u_i

Present the regression results, and provide a detailed discussion and interpretation of the estimated coefficients (i.e., intercept and slopes). Are all the results as expected?

Now re-estimate the linear regression model in Q.4. by including the swimming pool and fire place dummy variables pool and fireplace as in the following equation.

price_i= β₀+ β₁size_i + β₂age_i + β₃proximity_i+ β₄pool_i + β₅ fireplace_i + u_i

Discuss the implications of adding these two dummy variables into the regression model estimated in Q.4. in terms of the goodness-of-fit of your model.

Real estate economists have found that for many house price data sets, a more appropriate model has the dependent variable in natural logarithms, i.e. log(price).

Now estimate the following regression model:

log(price_i )= β₀ + β₁ log(size_i )+ β₂ age_i + β₃proximity_i+ β₄pool_i+ β₅ fireplace_i + u_i

Present the regression results and interpret the slope coefficients β₁ and β₄. Notice in this model that the size variable is included as an explanatory factor in natural logarithms.

Given your estimates in Q.6. test the null hypothesis at 1% level of significance that having a fireplace does not influence the house sale prices. Does your conclusion change at 10% level of significance? Show your hypothesis testing procedure.

Based on the multiple regression results you obtained in Q.6., test the joint significance of the full set of explanatory factors included in the regression at 5% level of significance.

Word Limit: 1500 words excluding appendices, figures and tables.

Attachment:- Data Set-2.xlsx