The scatterplot shows the four points (1,2), (2, 6), (4, 2) and (5,6) plotted in a 10x10 graphing window. Find the correlation and the equation of the time of best fit. regression line. r = ŷ = 2. Now investigate the influence of one more point on the correlation and the slope. Try each of these as the fifth point and record the new correlation and slope. Also note whether the new point has a small or large residual (NOTE: Add each point to the original four, one at a time, see what happens, and then remove that point. There are never more than 5 points in the plot!) Slope of the regression line Fifth Size of the point Description Correlation residual None the original four points N/A right in the center of the given points (3,4) also on the line, but far from the (8,6) other points only close to the line, but much farther away (10,7) above the center of the original (3,8) cluster nearby, but not consistent with the (1,7) apparent pattern farther away, and also not consistent (8,9) (10,0) farther and stranger... 3. A point that dramatically changes the apparent slope of the regression line is called an influential point. You need to be able to spot potential influential points in a scatterplot. What should you look for? 4. Originally there were only four points here. Suppose instead that we had started with 50 points clustered in essentially the same region and displaying an association of roughly the same strength and direction. Would our fifty-first point still be as influential? Where would you locate one additional point so influential that it changed the line as dramatically as (10,0) did above?
The scatterplot shows the four points (1,2), (2, 6), (4, 2) and (5,6) plotted in a 10x10 graphing window. Find the correlation and the equation of the time of best fit. regression line. r = ŷ = 2. Now investigate the influence of one more point on the correlation and the slope. Try each of these as the fifth point and record the new correlation and slope. Also note whether the new point has a small or large residual (NOTE: Add each point to the original four, one at a time, see what happens, and then remove that point. There are never more than 5 points in the plot!) Slope of the regression line Fifth Size of the point Description Correlation residual None the original four points N/A right in the center of the given points (3,4) also on the line, but far from the (8,6) other points only close to the line, but much farther away (10,7) above the center of the original (3,8) cluster nearby, but not consistent with the (1,7) apparent pattern farther away, and also not consistent (8,9) (10,0) farther and stranger... 3. A point that dramatically changes the apparent slope of the regression line is called an influential point. You need to be able to spot potential influential points in a scatterplot. What should you look for? 4. Originally there were only four points here. Suppose instead that we had started with 50 points clustered in essentially the same region and displaying an association of roughly the same strength and direction. Would our fifty-first point still be as influential? Where would you locate one additional point so influential that it changed the line as dramatically as (10,0) did above?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text:1. The scatterplot shows the four points (1,2), (2, 6), (4, 2) and (5,6)
plotted in a 10x10 graphing window. Find the correlation and the
equation of the fime of best fit. regression line.
r =
ŷ =
2. Now investigate the influence of one more point on the correlation and
the slope. Try each of these as the fifth point and record the new correlation and slope. Also
note whether the new point has a small or large residual (NOTE: Add each point to the
original four, one at a time, see what happens, and then remove that point. There are never
more than 5 points in the plot!)
Slope of the
regression line
Fifth
Size of the
point
Description
Correlation
residual
None
the original four points
N/A
right in the center of the given
points
(3,4)
also on the line, but far from the
other points
(8,6)
only close to the line, but much
farther away
(10,7)
above the center of the original
(3,8)
cluster
nearby, but not consistent with the
apparent pattern
farther away, and also not
(1,7)
(8,9)
consistent
(10,0)
farther and stranger...
3. A point that dramatically changes the apparent slope of the regression line is called an
influential point. You need to be able to spot potential influential points in a scatterplot. What
should you look for?
4. Originally there were only four points here. Suppose instead that we had started with 50 points
clustered in essentially the same region and displaying an association of roughly the same
strength and direction. Would our fifty-first point still be as influential? Where would you
locate one additional point so influential that it changed the line as dramatically as (10,0) did
above?
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