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Linear Models Examples

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Linear Models Examples
Curve-Fitting Project – Linear Model:
Average Sales Prices of new homes sold in the United States between 1964 and
2008
(LR-1) Purpose: To analyze the average sales prices of new homes sold in the United States from 1964 to
2008.
Data: The prices were retrieved from http://www.census.gov/const/uspriceann.pdf. I chose to use the prices between 1964 and 2008 as they showed a huge increase (More data was available (see link)).

Average sales prices of new homes sold in the US

Year

Time (seconds)

1964

$20,500.00

1968

$26,600.00

1972

$30,500.00

1976

$48,000.00

1980

$76,400.00

1984

$97,600.00

1988

$138,300.00

1992

$144,100.00

1996

$166,400.00

2000

$207,000.00

2004

$274,500.00

2008

$292,600.00

(LR-2)
Scatter plot:

The data seem to be linear and make sense since prices tend to increase as the economy goes downward and the years pass by.

(LR-3)

Line of best fit (Regression Line): y= 6377.185x – 12,538,215.035 where x= Year and y= Average sales prices (in Dollars)

(LR-4)
The slope of the equation is 6377.185 which is positive since prices of homes usually increase with time.
The slope tells us that the average price of homes increases by $6,377.185 every year. Since we are using 4 years increments, the prices increase at an average rate of 4*$6,377.185= $25,508.74 every 4 years. (LR-5)
Values of r2 and r:
From the above line of best fit, we can see that the coefficient of determination r2= 0.9499.
Since the slope of the regression line is positive r will be positive as well.
Therefore the correlation coefficient r = √0.9499 = 0.97.

We know that when r= 1, the correlation is considered a perfect positive correlation, and since our r=
0.97, it indicates that the linear relationship is very strong because it is very close to 1.

(LR-6)
Let’s predict the average price of a new home in 2012 and 2020. We plug in the year in place of the x.
When x= 2012 y= 6377.185*2012 – 12,538,215.035 y= $292,681.185
When x= 2020 y= 6377.185*2020 –

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