INSTRUCTIONS: Answer ALL the questions below with concise and clear answers. Note that 25% of your mark will be for quality of presentation, particularly compactness. Please don't include information that is not relevant to the questions asked. In exercises that include calculations/derivations, you must demonstrate your full derivation as no marks will be given for providing an answer (even a correct one) without explaining where it comes from. Include graphs where requested to support your answers. Marks may be deducted if graphs are not clearly marked. Illegible solutions may not be marked at all. Graphs (and tables, if used) should be as complete as possible and embedded into the rest of the exercises, i.e. not as appendices. You may discuss with your colleagues but the work you turn in must be your own. Be sure to include a cover sheet with a declaration, the course title and your signature (To be collected from the General Office, Skempton Building). Table 1 shows mean car ownership per capita and mean income per capita for 17 cities (urbanized areas) in the US. The data were obtained from the 2000 US Census. 1) Use these data to fit a linear model to test whether higher incomes are associated with higher car ownership. Calculate the estimated values of the model parameters, the standard errors of the estimated model parameters and the coefficient of determination (r²) of the model. Outline the important steps in the methodology you use. 2) According to the model, is income associated with car ownership? 3) Discuss the performance of the model, including necessary graphs to support your answer. Table 1

Urbanized area	Car ownership	Income (US dollars)
Bridgeport-Stamford, CT-NY	1.72	36977
Buffalo, NY	1.42	20020
Columbia, MO	1.63	19348
Concord, CA	1.91	38311
Fargo, ND-MN	1.71	20007
Grand Rapids, MI	1.73	21156
Elmira, NY	1.42	17283
Kenosha, WI	1.68	20556
Lancaster, PA	1.68	21175
Panama City, FL	1.68	19002
Waco, TX	1.56	16178
Ithaca, NY	1.33	18530
New York-Newark, NY-NJ-CT	1.16	26016
Danbury, CT-NY	1.89	28417
San Francisco-Oakland, CA	1.54	30239
San Jose, CA	1.97	32411
Washington, DC-VA-MD	1.60	31568