Examine the computation formula for r, the sample correlation coefficient. (a) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get the same (equivalent) result? Explain your answer. The result is the same because the formula is dependent on the symbols. The result is different because the formula is dependent on the symbols. The result is the same because the formula is not dependent on the symbols. The result is different because the formula is not dependent on the symbols. (b) If we have a set of x and y data values and we exchange corresponding x and y values to get a new data set, should the sample correlation coefficient be the same for both sets of data? Explain your answer. The result is different because the formula is not dependent on which values are the x values and which values are the y values. The result is the same because the formula is dependent on which values are the x values and which values are the y values. The result is different because the formula is dependent on which values are the x values and which values are the y values. The result is the same because the formula is not dependent on which values are the x values and which values are the y values. (c) Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.) (i) x 4 (ii) 3 5 4

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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.