26. Which of these are true and which are false? Explain why the false statements are wrong.a. If two variables have a correlation of 0.3 and you add 0.1 to every value of bothvariables, then the correlation will become 0.4.b. A correlation of 0.5 means that half of the points in the scatterplot fall in a linearpattern.c. If the correlation is close to negative one, then the regression line will have a negativeslope.d. The square of the correlation coefficient tells you the percentage of the variability in Ythat is explained by knowing X.e. An outlier in the scatterplot can heavily influence a regression line.f. An outlier that falls right on the regression line can still have an important effect on thecorrelation.g. The regression line is not appropriate for making predictions when X and Y have a non-linear relationship.h. If there is a linear pattern to the data, then linear regression can be appropriately used forextrapolation.i. If there is a non-linear relationship between x and y, then the correlation will always bezero.j. The correlation r measures both the direction and strength of a straight-line relationship.k. When the correlation between two variables is nearly negative 1, then there is a cause-and-effect relationship between them.1. A correlation close to negative one indicates there were no outliers on the scatterplot.m. If there is a linear pattern to the data and there are no outliers driving the regression, thenlinear regression can be appropriately used for predictions within the range of the data.MacBook Air

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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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26. Which of these are true and which are false? Explain why the false statements are wrong.
a. If two variables have a correlation of 0.3 and you add 0.1 to every value of both
variables, then the correlation will become 0.4.
b. A correlation of 0.5 means that half of the points in the scatterplot fall in a linear
pattern.
c. If the correlation is close to negative one, then the regression line will have a negative
slope.
d. The square of the correlation coefficient tells you the percentage of the variability in Y
that is explained by knowing X.
e. An outlier in the scatterplot can heavily influence a regression line.
f. An outlier that falls right on the regression line can still have an important effect on the
correlation.
g. The regression line is not appropriate for making predictions when X and Y have a non-
linear relationship.
h. If there is a linear pattern to the data, then linear regression can be appropriately used for
extrapolation.
i. If there is a non-linear relationship between x and y, then the correlation will always be
zero.
j. The correlation r measures both the direction and strength of a straight-line relationship.
k. When the correlation between two variables is nearly negative 1, then there is a cause-
and-effect relationship between them.
1. A correlation close to negative one indicates there were no outliers on the scatterplot.
m. If there is a linear pattern to the data and there are no outliers driving the regression, then
linear regression can be appropriately used for predictions within the range of the data.
MacBook Air

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Correlation is used to analyze the mutual relationship between two or more variables. The correlation coefficient is denoted by r. It can take any value from -1 to +1.

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