Drilling down beneath a lake in Alaska yields chemical evidence of past changes
ID: 3299132 • 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:
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 (mg/g) (96) -19.90 -19.84 -19.46 -20.20 (%) -20.71 -20.80 267 -20.86 271 -21.28 296 (mg/g) | (mg/g) | 104 114 143 (96) -21.63 222 -21.63 235 -21.19 -19.37 339 188 (a) Make a scatterplot of silicon (response) against isotope (explanatory) Isotope (%) Isotope (%) 400 350 300 250 200 150 100 Silicon (mg/g) 100 150 200 250 300 350 19.5 -20.0 -20.5 -21.0 -21.5 Silicon (mg/g) -22.0 -21.5-21.0-20.5-20.0-19.5-19.0Explanation / Answer
Let,
x = Isotope
y = silicon
x
y
-19.9
99
-19.84
104
-19.46
114
-20.2
143
-20.71
152
-20.8
267
-20.86
271
-21.28
296
-21.63
222
-21.63
235
-21.19
188
-19.37
339
Question a)
Scatterplot: First column third option
Weak negative association
Question b)
Outlier (-19.37, 339)
Question b)
By using excel ,
=correl(data set)
=-0.33
1st correlation = -0.33
2nd correlation = -0.78
Question c)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.3325699
R Square
0.1106027
Adjusted R Square
0.021663
Standard Error
80.140043
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
1
7986.735
7986.735
1.2435697
0.290865834
Residual
10
64224.265
6422.4265
Total
11
72211
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-488.3159
619.91178
-0.7877184
0.4491297
-1869.565405
892.9336128
X Variable 1
-33.579579
30.11204
-1.1151546
0.2908658
-100.6733861
33.51422741
y^ = -488.32 – 33.58x (with correlation)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.7800438
R Square
0.6084683
Adjusted R Square
0.5649648
Standard Error
47.509747
Observations
11
ANOVA
df
SS
MS
F
Significance F
Regression
1
31570.325
31570.325
13.986647
0.004626402
Residual
9
20314.584
2257.176
Total
10
51884.909
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-1376.0374
419.01009
-3.2840198
0.0094683
-2323.904095
-428.170758
X Variable 1
-75.724887
20.247986
-3.7398726
0.0046264
-121.529012
-29.9207611
y^ = -1376.04 – 75.72x
Regression Line:
4th graph
x
y
-19.9
99
-19.84
104
-19.46
114
-20.2
143
-20.71
152
-20.8
267
-20.86
271
-21.28
296
-21.63
222
-21.63
235
-21.19
188
-19.37
339
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