Drilling down beneath a lake in Alaska yields chemical evidence of past changes
ID: 3304065 • Letter: D
Question
Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon, left by the skeletons of single-celled creatures called diatoms measures the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look farther into the past. Here are data from 2300 to 12,000 years ago: Isotope Silicon Isotope Silicon Isotope Silicon (96) (mg/g) | (96) (mg/g) | (%) (mg/g) -19.90 95 |-20.71 156 |-21.63 226 -19.84 104 |-20.80 267 |-21.63 237 -19.46 118-20.86 271 21.19184 -20.20 13921.28 298-19.37 337Explanation / Answer
Answer:
a).
scatterplot: top left
moderate negative association
b).
correlation with outlier = -0.34
correlation without outlier = -0.78
c).
Regression with outlier
Y=-511.3-34.71 x
Regression Analysis
r²
0.117
n
12
r
-0.342
k
1
Std. Error
80.131
Dep. Var.
silicon
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,531.3086
1
8,531.3086
1.33
.2759
Residual
64,209.3580
10
6,420.9358
Total
72,740.6667
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=10)
p-value
95% lower
95% upper
Intercept
-511.3125
619.8398
-0.825
.4287
-1,892.4017
869.7768
isotope
-34.7055
30.1085
-1.153
.2759
-101.7915
32.3805
Regression without outlier
Y=-1395.0-76.66 x
Regression Analysis
r²
0.610
n
11
r
-0.781
k
1
Std. Error
47.961
Dep. Var.
silicon
ANOVA table
Source
SS
df
MS
F
p-value
Regression
32,352.4603
1
32,352.4603
14.06
.0046
Residual
20,702.2670
9
2,300.2519
Total
53,054.7273
10
Regression output
confidence interval
variables
coefficients
std. error
t (df=9)
p-value
95% lower
95% upper
Intercept
-1,394.9550
422.9894
-3.298
.0093
-2,351.8235
-438.0866
isotope
-76.6572
20.4403
-3.750
.0046
-122.8963
-30.4180
Graph: Bottom right
Regression Analysis
r²
0.117
n
12
r
-0.342
k
1
Std. Error
80.131
Dep. Var.
silicon
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,531.3086
1
8,531.3086
1.33
.2759
Residual
64,209.3580
10
6,420.9358
Total
72,740.6667
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=10)
p-value
95% lower
95% upper
Intercept
-511.3125
619.8398
-0.825
.4287
-1,892.4017
869.7768
isotope
-34.7055
30.1085
-1.153
.2759
-101.7915
32.3805
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