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 flfluctuations, prevailing

wage rates, and local prices. The data fifile 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 reflflect 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)

[5 marks] Plot a scatterplot of Big Mac prices with year 2003 as the predictor

variable. Add a line for y = x to this plot. How would you interpret points that

are on this line, above the line and below the line?

(b)

[5 marks] Identify the cities which you consider to have the highest increase or

decrease in the Big Mac price. You will fifind these R functions very useful for this

step: identify() and row.names().

(c)

[10 marks] Is a linear model the right one to fifit the Big Mac price data? If not,

what variable transformations would you consider appropriate? Give justifification

for your choice of transformation.

(d)

[20 marks] Fit a linear model with your chosen transformation using OLS estima

tion 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 effffect of coeffiffifficients on the untransformed response variable

in the untransformed version of the regression model.

(e)

[10 marks] Produce the ANOVA (Analysis of Variance) table for the SLR model

and interpret the results of the F-test. What is the coeffiffifficient of determination for

this model and how should you interpret this summary measure?

(f)

[10 marks] Assess the model fifit for the assumptions of a Normal Error Regression

Model. Are there any inflfluential points in your regression model and if yes, identify

these cities and the type of inflfluence they have on the model fifit.