Untitled Document

STEPS FOR CONDUCTING A SIMPLE LINEAR REGRESSION

1. Hypothesize a linear model

2. Obtain the least squares estimates of slope and intercept

3. Check the model assumptions;

linearity
constant variance
normally distributed error terms
independence of error terms

4. Check the usefulness of the model;

test & confidence intervals on slope
coefficient of correlation
coefficient of determination

5. Use the model for estimation & prediction

ACTIVITY

Suppose a fire insurance company wants to relate the amount of fire damage in major residentail fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city; a sample of 15 recent fires in this suburb is selected. The amount of damage, y, and the distance between the fire and the nearest fire station, x, are recorded for each fire. The results are given in the following table.

Distance from Fire Station x (miles)	Fire Damage y (thousands of dollars)
3.4	26.2
1.8	17.8
4.6	31.3
2.3	23.1
3.1	27.5
5.5	36.0
0.7	14.1
3.0	22.3
2.6	19.6
4.3	31.3
2.1	24.0
1.1	17.3
6.1	43.2
4.8	36.4
3.8	26.1

Use the following steps and Statlets window given above, to carry out a simple linear regression anlaysis on this data

Step 1. Enter the data:

Double click on "Col_1" and relace it with "Distance".

Double click on "Col_2" and relace it with "Damage".

Enter the data as below for the "distance" and "damage".

Step 2. Fit the model:

Select the "Summary" menu option and interpret the output.

Step 3. Model checking:

Select the "Fitted Model Plot" menu option and interpret the output.

Select the "R-Plots" menu option and interpret the output.

Select the "Residuals" menu option and interpret the output.

Step 4. Checking the usefulness of the model:

Select the "Summary" menu option.

Test the hypothesis that "intercept" is 0.

Test the hypothesis that "slope" is 0.

Report the coeeficient of correlation and coefficient of determination (R-squared) and interpret them.

Step 5. Use of the Model:

Select the "Predictions" menu option.

Click on the "Options" button.

To predict the fire damage if a major residential fire were to occur 3.5 miles from the nearest fir station, Type "3.5" in the box below "X".

Click "OK".

Interpret the predicted value and the 95% prediction interval and 95% confidence interval. Also discuss the difference between these two confidence intervals.