Distribution of “hammerpriceinpounds” and its (natural) logarithmic transformation in histograms.

You will be working on an original dataset collected for my project on the art market. It documents the prices paid at high profile auctions for ushabti (shabti, shawabti) figurines from ancient Egyptian tombs. We will be modelling hammer prices (in GB£) for these figurines depending on their characteristics, as well as market conditions.

1: Identify the three most expensive ushabtis in the dataset and describe their attributes. Are they statistical outliers? Do you think there may have been a mistake in recording the entries? If so, suggest a suitable remedy for dealing with these entries. (10 marks)

2: Display the distribution of “hammerpriceinpounds” and its (natural) logarithmic transformation in histograms. Explain whether you would use the raw data or the logarithmic transformation for OLS regression analysis. (10 marks)

3: There are 5 different categories of material. Create a single graph with boxplots comparing lnhammerprice for wooden, stone, and faience ushabtis. (10 marks)

4: Display the relationship between “lnhammerprice” and your “lowdate” in a scatterplot. Does the plot suggest a significant correlation between the variables? Describe the relationship in appropriate statistical language. (10 marks)

5: We have data from three auction houses: Sotheby’s, Christies, and Bonhams and two locations (London and New York). Use (appropriate) t-tests to explore the following hypotheses. Give a detailed explanation of your method and findings.
a) Christies sells more expensive ushabtis than Sotheby’s on average. (10 marks)
b) Higher priced ushabtis are traded in London (10 marks)

6: Use bivariate OLS regressions to explore the correlation between the following characteristics and lnhammerprice paid. Report all your findings in a single table. In each case carefully explain your findings and highlight the statistical significance in the table using the *-system (with a legend). (5 marks each, 20 marks overall)
a) lowdate
b) sizeincm
c) Year (i.e. is there a linear time trend in sales prices)
d) Whether an object has been “published” (i.e. is considered of scholarly importance)

7: Use multivariate OLS regression analysis to explore the effect of material on the hammer price. In your model use “lowdate” and “Size”, and “Year” as control variables and test whether wooden, metal, stone, and faience objects command a price premium (compared to composition / terracotta / other). 
a) Display your results in a table with all important information included and statistical significance highlighted. (10 marks) 
b) Explain your results in plain English. (10 marks)