1. Fitting Linear Models to Data
Section 1.4
Fitting Linear Models
to Data

2. EXAMPLE
The table below shows the census data for Spalding County, Georgia from 1960 through 2000.
Year
Pop (thous)
1960
35.4
1970
39.5
1980
47.9
1990
54.5
2000
58.4
Source: US Census Bureau

3. PLOT OF SPALDING COUNTY CENSUS DATA

4. AVERAGE RATE OF CHANGE
Definition: The average rate of change of a population P over a time interval is the change ΔP in the population divided by the length Δt of the time interval,

5. ACTUAL AND PREDICTED POPULTIONS
P(t)
(Predicted)
Discrepancy
P – P(t)
1960
35.4
1970
39.5
41.15
-1.65
1980
47.9
46.9 1
1990
54.5
52.65
1.85
2000
58.4

6. SUM OF SQUARES OF ERRORS
Definition: The phrase “Sum of Squares of Errors” is so common in data modeling that it is abbreviated SSE. Thus, the SSE associated with a data model based on n data points is defined by

7. AVERAGE SQUARED ERROR

8. AVERAGE ERROR
Definition: The average error in a linear model fitting n given data points is defined in terms of its SSE by
This formula says simply that the average error is the square root of the average of the squares of the individual errors.