A scatterplot contains four points: (−2,−2), (−1,−1), (0,0), and (1,1). A fifth point, (2,y), is to be added to the plot. Let r represent the correlation between x and y. a) Find the value of y so that r = 1. b) Find the value of y so that r = 0. c) Find the value of y so that r = 0.5. d) Find the value of y so that r = −0.5. e) Give a geometric argument to show that there is no value of y for which r = −1.
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.
A
to be added to the plot. Let r represent the
a) Find the value of y so that r = 1.
b) Find the value of y so that r = 0.
c) Find the value of y so that r = 0.5.
d) Find the value of y so that r = −0.5.
e) Give a geometric argument to show that there is no value of y for which r = −1.
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