Maria Trujillo
Prof. Betne
MAT 120.1605
November 3, 2008
PROJECT 2
CARBON DIOXIDE AND GLOBAL TEMPERATURE
Evidence of the reality of global warming continues to accumulate. Consistent with predictions of
the IPCC since 1990, global average temperatures have indeed been rising while atmospheric
CO2 increases at a rate of approximately 1.6ppm per year. Following table gives the average
temperature and CO2 concentration between 1960 and 2005.
Year
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Global average Temp
(o F)
57.2
57.1
56.9
57.0
57.3
57.2
57.7
57.7
57.7
58.0
CO2 concentration in
parts per million
(ppm)
315
320
324
334
340
348
354
361
370
375
1. Draw a scatter plot of CO2 concentration versus year. What is the shape of the graph?
The graph has a positive linear relation between CO2 concentration and the year. This means that
as the years will pass by the CO2 concentration will increase.
2. Use the above data to estimate the rate of change in the CO2 concentration between all two
consecutive years and find the average rate of change. Do your results support the fact that
is stated above the table (i.e. the atmospheric CO2 increases at rate of approximately
1.6ppm)?
Correlations
Co2
concentration in
Year
Year
Pearson Correlation
parte per million
1.000
Sig. (2-tailed)
N
Co2 concentration in parte
Pearson Correlation
per million
Sig. (2-tailed)
N
**. Correlation is significant at the 0.01 level (2-tailed).
.998**
.000
10
10
.998**
1.000
.000
1
10
Year
CO2 Concentration in
Rate of Change
Parts per Million (ppm)
y2 – y1
x2 – X 1
1960
315
1960-1965 = 5
5/5 = 1
1965
320
1965-1970 = 4
4/5 = 0.8
1970
324
1970-1975 = 10
10/ 5 = 2
1975
334
1975-1980 = 6
6/5 = 1.2
1980
340
1980-1985 = 8
8/5 = 1.6
1985
348
1985-1990 = 6
6/5 = 1.2
1990
354
1990-1995 = 7
7/5 = 1.4
1995
361
1995-2000 = 9
9/5 = 1.8
2000
370
2000-2005 = 5
5/5 = 1
2005
375
∑ of Rate of Change = 60
∑ Slopes = 12
x= ∑x
n
x = 12
x = 1.33
9
The rate of change in the CO2 concentration between CO2 concentration and consecutive years is
1.33 So my results do not support the fact that is stated in the table.
3. Use the fact that the atmospheric CO2 increases at a rate of approximately 1.6ppm to
write the equation of a straight line using CO2 concentration in 1960 as the base value and X
being the number of years since 1960. Then use the equation to predict the CO2
concentration for 2010.
Model Summary
Model
1
R
Adjusted R
Std. Error of the
Square
Estimate
R Square
.998a
.996
.995
1.413
a. Predictors: (Constant), Year
ANOVAb
Model
1
Sum of Squares
Regression
Residual
Total
df
Mean Square
3958.936
1
3958.936
15.964
8
1.995
3974.900
9
a. Predictors: (Constant), Year
b. Dependent Variable: CO2 Concentration in Parts per Million
F
1983.977
Sig.
.000a
Coefficientsa
Standardized
Unstandardized Coefficients
Model
1
B
(Constant)
Year
Coefficients
Std. Error
-2402.564
61.666
1.385
.031
Beta
t
.998
Sig.
-38.961
.000
44.542
.000
a. Dependent Variable: CO2 Concentration in Parts per Million
y-intercept = 315
y- intercept = 315
slope = 1.33
slope = 1.66
y = mx + b
y = mx + b
y = 1.3(50) + 315
y = 1.6(50) + 315
y = 65 + 315
y = 80 + 315
y = 380
y = 395
Using the fact that the atmospheric CO2 concentration increases at a rate of approximately 1.6ppm
the CO2 concentration for the year 2010 is 395ppm. But if I use the fact that the atmospheric CO2
concentration increases at a rate of approximately 1.3ppm the CO2 concentration for the year 2010
is 380ppm.
4. Draw a scatter plot of CO2 concentration versus the temperature values. What pattern do
you observe? What can you conclude from this graph about the relation between CO2
concentration and Global temperature?
5. Obtain equation of the regression line using CO2 as independent variable and
temperature as a dependent variable. Use the equation to predict the average global
temperature when the CO2 level becomes equal to 380 ppm.
ANOVAb
Variables Entered/Removedb
Model
1
Sum of Variables
Squares
RegressionModel
Residual 1
df Variables
Mean Square
Entered
.940
Removed
1
F
Method
.940
Sig.
.001a
27.222
CO2
.276
8
.035
Concentration in
. Enter
Total
1.216
9
Parts per Milliona
a. Predictors: (Constant), CO2 Concentration in Parts per Million
a. All requested variables entered.
b. Dependent Variable: Global Average Temperature
b. Dependent Variable: Global Average Temperature
Model Summary
Model
1
R
Adjusted R
Std. Error of the
Square
Estimate
R Square
.879a
.773
.744
.1858
a. Predictors: (Constant), CO2 Concentration in Parts per Million
Coefficientsa
Standardized
Unstandardized Coefficients
Model
1
B
(Constant)
CO2 Concentration in Parts
per Million
Std. Error
52.089
1.016
.015
.003
a. Dependent Variable: Global Average Temperature
Coefficients
Beta
t
.879
Sig.
51.279
.000
5.217
.001
y- intercept = 52.089
slope = .015
y = mx + b
y = .015(380) + 52.089
y = 5.7 + 52.089
y = 57.789
The average global temperature when CO2 level becomes equal to 380 ppm is 57.8.
6. Estimate the change in the global temperature value if the value of CO2 level increases by
2 units.
Years
Rate of Change
1960-1965
7
7/5 = 1.4
1965-1970
6
6/5 = 1.2
1970-1975
12
12/ 5 = 2.4
1975-1980
8
8/5 = 1.6
1980-1985
10
10/5 = 2
1985-1990
8
8/5 = 1.6
1990-1995
9
9/5 =1.8
1995-2000
11
11/5 = 2.2
2000-2005
7
7/5 = 1.4
∑ Rate of Change = 71
∑
x=∑x
n
x = 15.6
9
x = 1.73
The estimate change in temperature if the CO2 increases by 2 units is 1.73
= 15.6
7. Compute the residuals then draw a residual plot (plot of X vs. residuals) and
interpret the plot.
x
315
320
324
334
340
348
354
361
370
375
(y – y )
57.2 – 56.814 = 0.386
57.1 – 56.889 = 0.211
56.9 – 56.949 = -0.049
57.0 – 57.099 = -0.099
57.3 – 57.189 = 0.111
57.2 – 57.309 = -0.109
57.7 – 57.399 = 0.301
57.7 – 57.504 = 0.196
57.7 – 57.639 = 0.061
58.0 – 57.714 = 0.286
y
56.814
56.889
56.949
57.099
57.189
57.309
57.399
57.504
57.639
57.714
CO2 CONCENTRATION VS. RESIDUALS
.4
.3
.2
.1
RESIDUAL
0.0
-.1
-.2
310
320
330
340
350
360
370
380
CO2 Concentration in Parts per Million
Model Summary
Model
1
R
.045(a)
R Square
.002
Adjusted R
Square
-.123
Std. Error of
the Estimate
.185805
a Predictors: (Constant), CO2 Concentration in Parts per Million
According to the Box-Plot there is no a linear relation between the data because R is closer to 0.