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 –
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 –