# Simple Linear Regression Model

Practice Problems

a) Explain what is meant by " is an unbiased estimator of the parameter ".

b) Why is it desirable for a sample statistic to be unbiased?

c) and are unbiased estimators of ______ and ______ respectively.

6. Acu-Copiers sells and services the Acu-500 copying machine. As part of its standard service contract, the company performs routine service on this copier. They would like to be able to predict the time for a routine service based on the number of copiers to be serviced. Acu-Copiers collected the following data for 11 service calls.

Service

Call Number of

Copiers Serviced : X Number of

Minutes required :Y

1 4 100

2 2 60

3 5 140

4 7 190

5 1 40

6 3 80

7 4 100

8 5 130

9 2 70

10 4 110

11 6 150

Total 43 1170

a. Which is the response variable, Y, and which is the explanatory variable, X ?

b. Assuming a SLR model ( ) is appropriate, find the least squares fitted regression equation.

c. For this problem, give the practical interpretations (if possible) for b1 and b0. If it is not possible, explain why.

d. The error term in the statistical model for this problem describes the effects of many factors on service time. Give 2 specific examples of such factors.

#### Solution Preview

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Practice Problems continued

5.

a) Explain what is meant by " is an unbiased estimator of the parameter ".

A statistic used to estimate a population parameter is unbiased if the mean of the sampling distribution of the statistic is equal to the true value of the parameter being estimated. If is an estimate of a population parameter , then if E( ) = , is said to be an unbiased estimate of .

When we actually run the experiment and observe the data, the observed value (a single number based on the data ) is the estimate of the parameter . The (random) error is difference between the estimator and the parameter: - . The expected value of the error is known as the bias: Bias( ) = E( - ).Thus, the estimator is said to be unbiased if the bias is 0 .Equivalently if the expected value of the estimator is the parameter being estimated: E( ) = .

Thus the difference between an estimator's expected value and the true value of the parameter being estimated is called the bias. An estimator or decision rule having nonzero ...

#### Solution Summary

Simple linear regression with estimation of regression coefficients. The solution also contain calculation of slope, intercept, correlation, residual, r-square, coefficient of determination, and regression coefficients with a scatter diagram.