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ECOM90009 Quantitative Methods For Business

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i.Present appropriate descriptive statistics for the quantitative variables that you have downloaded. Remember to only provide appropriate statistics (mean, median, standard deviation, variance, min, max). Briefly describe in words what these descriptive statistics show, paying attention to the measures of central location (and thus symmetry/skewness) and the range.
ii.Present appropriate graphs of the relationship between house prices (our outcome of interest) and the four quantitative variables in the sample that theory and common sense would suggest will affect prices: lot size, number of bedrooms, number of bathrooms, and number of garages. Provide a brief description of what your graphs show. Do the relationships between the variables look linear or not?
iii.Estimate the relationship between house prices and the four quantitative variables that you considered in part (ii) using OLS. Write down the equation for the population model you are estimating. Report the estimates for your model in a table (Excel output table is fine) and write down the estimated model. Provide a full interpretation in words for each of the slope coefficients that you have estimated, paying particular attention to whether the relationships are significant or not. Finally, comment on the fit of the model you have estimated while briefly explaining and interpreting the goodness of fit measures.
iv.Suppose a house price owner in the area is thinking of building an additional bathroom before selling his house to achieve a higher price. However, since building a bathroom is quite costly it would only be worthwhile if it would increase the house price by over 16,000 CAD. Undertake a t-test to check whether the owner should build the additional bathroom or not. Do the six steps of the test and use the Excel output to help you construct the test statistic. (You can assume that all the required conditions hold.)
v.The model in part assumes that the price effect of an additional bathroom does not depend on the size of the house. While we don't have information on the size of the house, we have information on the size of the lot which we can use as a proxy variable  for house size. Create an interaction variable (bath_size = bath*lot_siz in Excel) and then re-estimate the model from part (iii) including the new interaction variable (i.e. in addition to the quantitative variables and intercept which were present in the model in Report the Excel output table of estimation results.

Write down the estimated model and interpret the coefficient on the interaction term. Find the expression for the effect of an additional bathroom on house price and then compute this effect for a house of average lot size. Interpret this result.

vi.List the five required conditions for using Ordinary Least Squares. Which of these required conditions can you check for your particular model estimated in part (v)? For those required conditions that you cannot check, describe why they cannot be checked. For the required conditions you can check, provide evidence of whether the required conditions hold or not. For any required conditions that you do not believe to hold here, briefly describe the specific consequences for your OLS results.
vii.Do you think we have multicollinearity in the model? Check the signs for multicollinearity to explain your answer.
viii.The data set contains an additional indicator variable that describes whether the house has a basement. We would think that this is a factor that may affect the price of a house and should therefore be included in the model.

Re-estimate the relationship for house prices from part (v) adding the indicator variable on basement as a regressor (i.e. in addition to your quantitative variables, interaction variable and intercept in part (v)). Report the estimates for your model in a table (Excel output table is fine) and write down the estimated model.

Provide a full interpretation of the coefficient for the newly included nominal variable. Comment on the fit of the model you have just estimated and compare it to the fit of the model from part (v). Using the Excel output, what can you say about the validity of the model?

ix.Using your estimates from part (viii), construct a point prediction for the price of a house with the following fairly typical characteristics: lot size of 5000 square feet, 3 bedrooms, 1 bathroom and 1 garage. Assume the house has no basement. Then construct a point prediction for the price of a house with the same characteristics as before, but with a basement now. Compare the two predictions and briefly discuss what you find.
x.Think of a question from finance, marketing, management, economics or accounting that can be answered with a multiple regression analysis. Write down the question, what data you would need to collect (what variables) and the population model that you would estimate. Briefly explain how the OLS estimates would help you answer your question.
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