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scs099
03-01-2006, 09:20 AM
Can anybody help me come up with the answers and how to solve these?

We estimate the mileage of a tank of gas for a hybrid car for inner-city driving as:

Distance in miles = alpha + beta*gallons of gas

where distance is in US miles and gas is in gallons (US). The ordinary least squares regression parameters are alpha hat = -2 and beta hat = 15. To use the regression equation in Europe, we express distance in kilometers and gas in liters. For this problem, as that 2 kilometers = 1 US mile and 3 liters = 1 US gallon.

If Y = 100 miles, it equals 200 kilometers
If X = 10 gallons, it equals 30 liters

For the regression equation using distance in kilometers and gas in liters, what is the ordinary least squares estimator B hat?

A. 5 B. 10 C. 15 D.22.5 D 30

Same question but for alpha hat.

A. -2/3 B. -1 C. -2 D. -4 E. -6

Peter Lemonjello
03-01-2006, 03:01 PM
This is just a unit conversion problem.

Here's some questions to help you along:

What are the units of alpha hat? What would you do to convert them to the "metric" units of the problem?

scs099
03-06-2006, 09:36 AM
I'm still confused on this one.

Peter Lemonjello
03-06-2006, 06:47 PM
Ok. The units of Alpha are miles. To convert miles to "Kilometers" multiply by 2 "Kilometers" / mile.

-2 x 2 = =4. So the answer to the second question is D.