Q T3.112. Drilling down beneath a lake in ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 3: Q T3.112. (page 202)

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, is a measure of 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 further into the past. Here is a scatterplot of data from $2300$ to $12, 000$ years ago:
(a) Identify the unusual point in the scatterplot. Explain what鈥檚 unusual about this point.
(b) If this point was removed, describe the effect on i. the correlation.
ii. the slope and y-intercept of the least-squares line.

Short Answer

Expert verified

Part (a) Point $A$ can be described as an outlier/unusual point since it falls outside of the overall pattern.

Part (b) (i) Correlation will increase.

Part (b) (ii) The $Y -$ intercept increase when the extreme value is removed from the scatter plot.

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Concept

A regression line shows how an explanatory variable $x$ affects a response variable $y$ You can use a regression line to forecast the value of $y$ for any value of $x$ by plugging this $x$ into the equation of the line.

Part (a) Step 3: Explanation

Point $A$ (value corresponding to isotope value $- 19.3$ and silicon value of $345$ is extreme in both the $X$ and $Y$ directions, with no other point near it, as shown in the scatter plot. As a result, it drags the regression line inward.

Part (b) (i) Step 1: Explanation

We can see that point $A$ is an outlier from portion $(A)$

When point $A$ is eliminated from the scatter plot, the remaining points are more tightly grouped in a linear pattern, increasing correlation.

Part (b) (ii) Step 1: Explanation

Point $A$ (Value corresponding to isotope value $- 19.3$ and silicon value of $345$ is extreme in both the $X$ and $Y$ directions, with no other point in the vicinity. As a result, it drags the regression line inward. When the extreme value, which corresponds to the greater value of silicon, is removed, the slope of the regression line decreases as it approaches the $X -$ axis. When the extreme value is eliminated from the scatter plot, the $Y -$ intercept increases.