Present an argument that var should be proportional

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The following data represent travel times in a downtown area of a certain city. The independent, or input, variable is the distance to be traveled.

Distance(miles) 5 1 1.5 2 3 4 5 6 8 10
Travel Time(minutes) 15 15.1 16.5 19.9 27.7 29.7 26.7 35.9 42 49.4

Assuming a linear relationship of the form

Y = α + βx + e

between Y , the travel time, and x, the distance, how should we estimate α and β? To utilize the weighted least squares approach we need to know, up to a multiplicative constant, the variance of Y as a function of x. We will now present an argument that Var(Y) should be proportional to x.

Reference no: EM13903654

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