Concerns about global warming have led to studies of the relationship between gl
ID: 3227020 • Letter: C
Question
Concerns about global warming have led to studies of the relationship between global temperature and the concentration of CO2. Listed below are the concentrations of CO2 in ppm (parts per million) and temperatures in Celsius [based on data from the Earth Policy Institute]. Is there a linear relationship between temperature and the concentration of CO2 at = 0.05? [fyi: safe is listed as 350 ppm]
CO2 314 317 320 326 331 339 346 354 361 369
Temperature 13.9 14 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4
a) r = ________
b) Critical value(s) = ___________
c) If there is a linear correlation, state the equation of the line: _________________________ [please don’t write y = mx + b. I want the equation for this study]
d) If there is a linear correlation, determine the predicted CO2 levels if the temperature rises to 14.8 degrees Celsius. ___________
Explanation / Answer
Answer:
Concerns about global warming have led to studies of the relationship between global temperature and the concentration of CO2. Listed below are the concentrations of CO2 in ppm (parts per million) and temperatures in Celsius [based on data from the Earth Policy Institute]. Is there a linear relationship between temperature and the concentration of CO2 at = 0.05? [fyi: safe is listed as 350 ppm]
CO2 314 317 320 326 331 339 346 354 361 369
Temperature 13.9 14 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4
a) r = 0.8920
Correlation Matrix
co2
temp
co2
1.000
temp
0.8920
1.000
10
sample size
± .632
critical value .05 (two-tail)
± .765
critical value .01 (two-tail)
b) Critical value(s) r = (-0.632, 0.632)
since calculated r=0.892 > 0.632, correlation is significant.
c) If there is a linear correlation, state the equation of the line:
CO2 = 72.8743*Temp -694.9281
[please don’t write y = mx + b. I want the equation for this study]
Regression Analysis
r²
0.796
n
10
r
0.892
k
1
Std. Error
9.243
Dep. Var.
co2
ANOVA table
Source
SS
df
MS
F
p-value
Regression
2,660.6389
1
2,660.6389
31.14
.0005
Residual
683.4611
8
85.4326
Total
3,344.1000
9
Regression output
confidence interval
variables
coefficients
std. error
t (df=8)
p-value
95% lower
95% upper
Intercept
-694.9281
185.0619
-3.755
.0056
-1,121.6817
-268.1746
temp
72.8743
13.0585
5.581
.0005
42.7613
102.9872
d) If there is a linear correlation, determine the predicted CO2 levels if the temperature rises to 14.8 degrees Celsius. ___________
when co2=14.8,
predicted CO2 = 72.8743*14.8 -694.9281
=383.61
Correlation Matrix
co2
temp
co2
1.000
temp
0.8920
1.000
10
sample size
± .632
critical value .05 (two-tail)
± .765
critical value .01 (two-tail)
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