Fitting Linear Models

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Section 1.4

• Fitting Linear Models
• to Data

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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
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PLOT OF SPALDING COUNTY CENSUS DATA
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AVERAGE RATE OF CHANGE
Definition The average rate of change of a
population P over a time interval is the change
?P in the population divided by the length ?t of
the time interval,
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ACTUAL AND PREDICTED POPULTIONS
t P (Actual) P(t) (Predicted) Discrepancy P P(t)
1960 35.4 35.4 0
1970 39.5 41.15 -1.65
1980 47.9 46.9 1
1990 54.5 52.65 1.85
2000 58.4 58.4 0
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SUM OF SQUARESOF 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
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AVERAGE SQUARED ERROR
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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.