Untitled Document

STEPS FOR CONDUCTING A MULTIPLE LINEAR REGRESSION

1. Hypothesize a linear model

2. Obtain the least squares estimates of slope and intercept parameters

3 & 4. Check the model assumptions;

linearity
constant variance
normally distributed error terms
independence of error terms

5. Check the usefulness of the model;

test & confidence intervals on the parameters
multiple coefficient of determination
adjusted multiple coefficient of determination

6. Use the model for estimation & prediction

ACTIVITY

Suppose a property appraiser wants to model the relationship between the sale price of a residential property in a mid-size city and the following three independent variables: appraised land value of the property, appraised value of improvements (home value), and area of the living space on the property (home size). The resulting data are given in the following table:

Property #	Sale Price (y)	Land Value	Improvements Value	Area
1	68,900	5,960	44,967	1,873
2	48,500	9,000	27,860	928
3	55,500	9,500	31,439	1,126
4	62,000	10,000	39,592	1,265
5	116,500	18,000	72,827	2,214
6	45,000	8,500	27,317	912
7	38,000	8,000	29,856	899
8	83,000	23,000	47,752	1,803
9	59,000	8,100	39,117	1,204
10	47,500	9,000	29,349	1,725
11	40,500	7,300	40,166	1,080
12	40,000	8,000	31,679	1,529
13	97,000	20,000	58,510	2,455
14	45,500	8,000	23,454	1,151
15	40,900	8,000	20,897	1,173
16	80,000	10,500	56,248	1,960
17	56,000	4,000	20,859	1,344
18	37,000	4,500	22,610	988
19	50,000	3,400	35,948	1,076
20	22,400	1,500	5,779	962

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

Step 1. Enter the data:

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

Double click on "Col_2" and relace it with "Sale Price".

Double click on "Col_3" and relace it with "Land Value".

Double click on "Col_4" and relace it with "Improvements".

Double click on "Col_5" and relace it with "Area".

Enter the data for each one of the vaiables.

Step 2. Fit the model:

Select the "Model Fit" menu option, report the least squares estimates of the parameters and interpret the them.

Step 3 & 4. Model checking:

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

Click on the "Options" button select a smoothing technique.

Click "OK".

Step 5. Checking the usefulness of the model:

Select the "Model Fit" menu option.

Test the hypothesis that "intercept" is 0.

Test the hypotheses that each one of teh slope parameters is 0.

Report "multiple coefficient of determination (R-squared)" and "adjusted multiple coefficient of determination and interpret them in the context of the problem.

Select the "Correlations" menu option and interpret the pairwise correlations. Which one of the independent variables is highly correlated with the sale price? Is there a high correlation among the independent variables?

Select the "Coefficients" menu option. Report 95% confidence intervals for each one of the parameters and interpret them.

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