# Simple Linear Regression Questions

Your company builds roads, bridges, schools and other multi-million dollar public construction projects. Competitive bids are made for the contracts to undertake these projects. For each project there are three costs:

a) the best estimate of what the project will cost your company to complete, made before a bid is submitted;

b) the "adjusted" cost on which the company bases its bid; this cost is the best estimate plus or minus a percentage which reflects how much your company wants to win the contract, and is also made before a bid is submitted;

c) on those projects for which your company is the winning bidder, the actual cost of completing the project; this is calculated after the project is completed.

You want to know whether the estimates of costs that are made prior to the bidding process are accurate predictors of the actual costs of completed projects.

Explain how you would use a simple linear regression model to answer that question. In your explanation, address the following questions:

a) How would you calculate the slope of the line?

b) How would you test the significance of the slope of the line?

c) How would you interpret the result of the test in b)?

d) Repeat a), b) and c) for the coefficient of correlation.

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#### Solution Preview

Your company builds roads, bridges, schools and other multi-million dollar public construction projects. Competitive bids are made for the contracts to undertake these projects. For each project there are three costs:

a) the best estimate of what the project will cost your company to complete, made before a bid is submitted;

b) the "adjusted" cost on which the company bases its bid; this cost is the best estimate plus or minus a percentage which reflects how much your company wants to win the contract, and is also made before a bid is submitted;

c) on those projects for which your company is the winning bidder, the actual cost of completing the project; this is calculated after the project is completed.

You want to know whether the estimates of costs that are made prior to the bidding process are accurate predictors of the actual costs of completed projects.

Explain how you would use a simple linear regression model to answer that question. In your explanation, address the following questions:

You would make a regression model using the actual cost as the dependent (y) variable and either the estimate or adjusted estimate as the independent (x) variable. It is possible to make a regression model with two independent variables (so you could use the estimate and the adjusted ...