Answer the following questions about the relationships between pairs of variables and the value: be the correct answer for more than one question. 1. Which data set indicates the strongest positive linear relationship between its two variables? the x, y data set v Choose one the x, y data set the u, v data set the w, t data set the m, n data set 2. For which data set is the sample correlation coefficient r equal to 1? 3. For which data set is the sample correlation coefficient r closest to -1? 4. For which data set is the sample correlation coefficient r closest to 0? Choose one
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.
Identify the data set that indicates the strongest positive linear relationship between two variables.
The data set for which there is strongest positive linear relationship between two variables is clearly between the variables u and v that is figure 2 because most of the given points are in the straight line and also the regression line is moving towards upper right from left of the x– axis which indicates that there is strongest positive linear relationship between the variables.
Thus, the data set that indicates the strongest negative linear relationship between two variables is u and v data set.
Identify the data set for which the sample correlation coefficient closest to 1.
The data set for which the sample correlation coefficient is closest to 1 is the scatter plot between the variables w and t that is Figure 3 because all of the points are very close together around the straight line and also the regression line is moving towards upper right from the left of the x– axis it indicates that sample correlation between the variables is very close to 1.
Thus, the data set for which the sample correlation coefficient is closest to 1 is w, t data set
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