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 global temperature and CO2 concentrations between
1960 and 2005.
Year
Global average
Temp (o F)
CO2 concentration in
parts per million (ppm)
1960
57.2
315
1965
57.1
320
1970
56.9
324
1975
57.0
334
1980
57.3
340
1985
57.2
348
1990
57.7
354
1995
57.7
361
2000
57.7
370
2005
58.0
375
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
1. Draw a scatter plot of CO2 concentration versus year. What is the shape of
the graph?
The graph has the shape of a line.
CO2 CONCENTRATION vs. YEAR
380
370
360
350
340
330
320
310
1950
1960
1970
1980
1990
2000
2010
Year
CORRELATIONS
1
CO2
Concentration
ppm
.998(**)
.
.000
10
10
Year
Year
Pearson Correlation
Sig. (2-tailed)
N
CO2 Concentration ppm
Pearson Correlation
Sig. (2-tailed)
N
.998(**)
.
10
10
** Correlation is significant at the 0.01 level (2-tailed).
REGRESSION
1
.000
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
Variables Entered/Removed(b)
Model
1
Variables
Entered
Year(a)
Variables
Removed
.
Method
Enter
a All requested variables entered.
b Dependent Variable: CO2 Concentration ppm
Model Summary
Model
1
R
.998(a)
R Square
.996
Adjusted R
Square
.995
Std. Error of
the Estimate
1.413
a Predictors: (Constant), Year
ANOVA(b)
Model
1
Regression
Sum of
Squares
3958.936
df
1
Mean Square
3958.936
Residual
15.964
8
1.995
F
1983.977
Sig.
.000(a)
t
Sig.
-38.961
.000
44.542
.000
Total
3974.900
9
a Predictors: (Constant), Year
b Dependent Variable: CO2 Concentration ppm
Coefficients(a)
Unstandardized
Coefficients
Model
1
(Constant
)
Year
B
Std. Error
-2402.564
61.666
1.385
.031
a Dependent Variable: CO2 Concentration ppm
Standardized
Coefficients
Beta
.998
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
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 a rate of approximately 1.6ppm)?
Slope (m), when x: year and y: CO2
(320-315) / (1965-1960) = 5/5 = 1
(334-324) / (1975-1970) = 10/5 = 2
(348-340) / (1985-1970) = 8/5 = 1.6
(361-354) / (1995-1990) = 7/5 = 1.4
(375-370) / (2005-2000) = 5/5 = 1
Then (1+2+1.6+1.4+1)/5= 7/5 =1.4ppm.
The results are closer to 1.6, so it support that the atmospheric CO2 increases at
a rate of approximately 1.6ppm.
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
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.
y = 1.6x+b

If x = 1960 and y = 315; then 315 = 1.6(1960) + b
b = 315-3136 then b = -2821

Then for x = 2010: y = 1.6(2010) – 2821 = 3216 – 2821
y = 395ppm.
In 2010 the CO2 concentration will be 395ppm.
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?
There is a linear relation between CO2 concentration and temperature the one that is
confirm by the data r=0.879.
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
CO2 CONCENTRATION vs. TEMPERATURES
58.2
58.0
57.8
57.6
57.4
57.2
57.0
56.8
310
320
330
340
350
360
370
380
CO2 Concentration ppm
CORRELATIONS
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
** Correlation is significant at the 0.01 level (2-tailed).
CO2
Concentration
ppm
1
Global Average
Temperature
.879(**)
.
.001
10
10
.879(**)
1
.001
.
10
10
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
REGRESSION
Variables Entered/Removed(b)
Model
1
Variables
Removed
Variables Entered
CO2 Concentration
ppm(a)
Method
.
Enter
a All requested variables entered.
b Dependent Variable: Global Average Temperature
Model Summary
Model
1
R
.879(a)
R Square
.773
Adjusted R
Square
.744
Std. Error of
the Estimate
.1858
a Predictors: (Constant), CO2 Concentration ppm
ANOVA(b)
Sum of
Squares
Model
Regressio
n
Residual
df
Mean Square
.940
1
.940
.276
8
.035
F
Sig.
27.222
.001(a)
Total
1.216
9
a Predictors: (Constant), CO2 Concentration ppm
b Dependent Variable: Global Average Temperature
Coefficients(a)
Unstandardized
Coefficients
Model
(Constant)
B
52.089
CO2
Concentration
.015
ppm
a Dependent Variable: Global Average Temperature
Standardized
Coefficients
Std. Error
1.016
.003
t
Sig.
Beta
.879
51.279
.000
5.217
.001
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
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.
From the data, the constant coefficient is 52.089 and the CO2 coefficient is 0.015,
and y=0.015x +52.089. Then y = 0.015(380)+52.089 = 5.7+52.089, y = 57.789.
The average global temperature when CO2 level becomes equal to 380ppm is
57.789 ºF.
6. Estimate the change in the global temperature value if the value of CO2 level
increases by 2 units.
If the CO2 level increases in 1 unit then the global temperature increases in 0.015
(slope), so if it increases in 2 units the global temperature would increase in:
2(0.015)=0.03.
7. Compute the residuals then draw a residual plot (plot of X vs. residuals) and
interpret the plot.
CO2 conc. (x)
Global Temp. (y)
y=0.015x+52.089
Residuals (y-y)
315
57.2
56.814
0.386
320
57.1
56.889
0.211
324
56.9
56.949
-0.049
334
57.0
57.099
-0.099
340
57.3
57.189
0.111
348
57.2
57.309
-0.109
Astrid Avalos
MAT120.1605
November 3, 2008.
Assignment 3
354
57.7
57.399
0.301
361
57.7
57.504
0.196
370
57.7
57.639
0.061
375
58.0
57.714
0.286
CO2 CONCENTRATION VS. RESIDUALS
.4
.3
Residuals
.2
.1
0.0
-.1
-.2
310
320
330
340
350
360
370
380
CO2 Concentration ppm
Model Summary
Model
1
R
R Square
Adjusted R
Square
Std. Error of
the Estimate
.045(a)
.002
-.123
.185805
a Predictors: (Constant), CO2 Concentration ppm
According to the data r is close to 0, then there is no linear relation between x
and residuals.