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.

Assuming a linear relationship of the form

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.

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Distance (miles) .5 1 1.5 2 3 4 5 6 8 10 Travel time (minutes) 15.0 15.1 16.5 19.9 27.7 29.7 26.7 35.9 42 49.4