Q 67. Bird colonies Return to the data... [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 67. (page 196)

Bird colonies Return to the data of Exercise $53$ on sparrow hawk colonies. We鈥檒l use these data to illustrate influence.
(a) Make a scatterplot of the data suitable for predicting new adults from the percent of returning adults. Then add two new points. Point A: $10 %$ return, $15$
new adults. Point B: $60 %$ return, $28$ new adults. In which direction is each new point an outlier?
(b) Add three least-squares regression lines to your plot: for the original $13$ colonies, for the original colonies plus Point $A$ , and for the original colonies
plus Point $B$ Which new point is more influential for the regression line? Explain in simple language why each new point moves the line in the way your graph shows.

Short Answer

Expert verified

Part (b) Point $A$ is more influential because the least-squares regression line deviates more strongly from the line with the original points where $A$ is included.

Part (a)

Step by step solution

Part (a) Step 1: Given information

Percent return	74	66	81	52	73	62	52	45	62	46	60	46	38
New adults	5	6	8	11	12	15	16	17	18	18	19	20	20

Part (a) Step 2: Concept

A regression line is a straight line that depicts the relationship between an explanatory variable $x$ and a response variable y. By entering any value of $x$ into the equation of the line, you may use a regression line to anticipate the value of y for any value of $x$

Part (a) Step 3: Explanation

On the horizontal axis, we plotted $%$ return (the explanatory variable), and on the vertical axis, we plotted new adults (the response variable).

The scatter plot for the provided data is shown below.

The scatter plot shows this. Outliers are denoted as points A and B. In the X direction of the scatterplot, point A is the outlier. Thus, the required scatterplot is drawn.

Part (b) Step 1: Explanation

The consequences of deleting each of these points from the correlation and regression line are shown in the diagram below. Two further regression lines are added to the graph, one calculated after adding point $A$ and the other calculated after adding point B. It can be observed that adding point $A$ to the line causes it to shift quite a bit. Point $A$ has a considerable influence on the position of the regression line due to its extreme position on the percent scale. Point $A$ is the scatterplot's outlier in the $X -$ direction. Adding a point, on the other hand, has little effect on the regression line.