Drilling down beneath a lake in Alaska yields chemical evidence of past changes
ID: 3229219 • 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:
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(b) Find the single outlier in the data. This point strongly influences the correlation. What is the correlation with this point? (Round your answer to two decimal places.)
Isotope(%) Silicon
(mg/g) Isotope
(%) Silicon
(mg/g) Isotope
(%) Silicon
(mg/g) 19.90 97 20.71 152 21.63 224 19.84 106 20.80 267 21.63 235 19.46 114 20.86 271 21.19 184 20.20 139 21.28 296 19.37
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(b) Find the single outlier in the data. This point strongly influences the correlation. What is the correlation with this point? (Round your answer to two decimal places.)
Explanation / Answer
Correlation coefficient r for the data without removing any outliers is r=0.3462
Step 1: Find XY , X2 and Y2 as it was done in the table below.
Step 2: Find the sum of every column to get:
X=246.87 , Y=2418 , XY=49990.38 , X2=5085.8161 , Y2=558558
Step 3: Use the following formula to work out the correlation coefficient.
r r = nXYXY[nX2(X)2][nY2(Y)2]= 1249990.38246.872418[125085.8161246.872][1255855824182]0.3462
Outlier is the value of (-19.37,333)
r after removing outlier is r=0.7788.
Explanation:
Find XY , X2 and Y2 as it was done in the table below.
Step 2: Find the sum of every column to get:
X=227.5 , Y=2085 , XY=43540.17 , X2=4710.6192 , Y2=447669
Step 3: Use the following formula to work out the correlation coefficient.
r r = nXYXY[nX2(X)2][nY2(Y)2]= 1143540.17227.52085[114710.6192227.52][1144766920852]0.7788
X Y XY XX YY 19.90 97 1930.3 396.01 9409 20.71 152 3147.92 428.9041 23104 21.63 224 4845.12 467.8569 50176 19.84 106 2103.04 393.6256 11236 20.80 267 5553.6 432.64 71289 21.63 235 5083.05 467.8569 55225 19.46 114 2218.44 378.6916 12996 20.86 271 5653.06 435.1396 73441 21.19 184 3898.96 449.0161 33856 20.20 139 2807.8 408.04 19321 21.28 296 6298.88 452.8384 87616 19.37 333 6450.21 375.1969 110889Related Questions
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