Drilling down beneath a lake in Alaska yields chemical evidence of past changes

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:

(a) Make a scatterplot of silicon (response) against isotope (explanatory).

Ignoring the outlier, describe the direction, form, and strength of the relationship. The researchers say that this and relationships among other variables they measured are evidence for cyclic changes in climate that are linked to changes in the sun's activity.

weak positive associationmoderate positive association    strong positive associationweak negative associationmoderate negative associationstrong negative association

Isotope
(%) Silicon
(mg/g) Isotope
(%) Silicon
(mg/g) Isotope
(%) Silicon
(mg/g) 19.90 95 20.71 156 21.63 226 19.84 104 20.80 265 21.63 237 19.46 118 20.86 271 21.19 184 20.20 143 21.28 298 19.37 335

Explanation / Answer

(a)
The first plot (top left) is the correct scatterplot.
Silicon is the response variable and isotope is explanatory variable so, isotope is on x-axis and silicon is on y-axis.
We see that there is decrease in silicon with increase in isotope with high negative slope. So, there is strong negative association.

(b)
The single outlier in the data is Isotope = 19.37   and Silicon = 335
The correlation of Isotope and Silicon including this outlier point is -0.35
The correlation of Isotope and Silicon excluding this outlier point is -0.78

(c)
The regression line including this outlier point is y = -512.65 - 34.77x
The regression line excluding this outlier point is y = -1386.65 - 76.26x

The graph on the down right is correct.

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