The international bank UBS regularly produces a report (UBS, 2009) on prices and earnings in major cities throughout the world. Three of the measures they include are prices of 1kg of rice, a 1kg loaf of bread and the price of a Big Mac. An interesting feature of the prices they report is measured in the minutes of labor required for a 'typical' worker in that location to earn enough money to purchase the commodity. Using minutes of labor corrects at least in in part for currency fluctuations, prevailing wage rates, and local prices. The data file includes measurements for rice, bread and big mac from the 2003 and 2009 reports. The year 2003 was before the GFC and the year 2009 which is after the GFC and so would reflect changes in prices due to this recession.

You may access the dataset from the 'ALR4' package and load the data from this package using the data(UBSprices) command.

(a)Is a linear model the right one to fit the Big Mac price data? If not, what variable transformations would you consider appropriate? Give justification for your choice of transformation.

(b) Fit a linear model with your chosen transformation using OLS estimation method. Write out the mathematical expression for the functional form of your model using both the transformed variables and the untransformed original variables. Interpret the effect of coefficients on the untransformed response variable in the regression model.

(c) Produce the ANOVA (Analysis of Variance) table for the SLR model and interpret the results of the F-test. What is the coefficient of determination for this model and how should you interpret this summary measure?

(d)Assess the model fit for the assumptions of a Normal Error Regression Model. Are there any influential points in your regression model and if yes, identify these cities and the type of influence they have on the model fit.