In a study measuring the relationship between height in centimeters and annual income in dollars, it has been determined that for Group 1, r2 =0.15 and for Group 2, r2 =0.10 where r denotes the correlation between the two variables. Least-squares regression lines are fitted to the observations from each group. Which of the following statement is true: A. There could be a positive relationship between the two variables for Group 1 and a negative relationship between the two variables for Group 2 B. The sum of the residuals for Group 1 is greater than the sum of the residuals for Group 2. C. Measuring the height in inches would increase the value of r2 for both groups. D. None of the answer options is true Can you also explain the difference between r and r2, and why least square regressions are used?
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.
In a study measuring the relationship between height in centimeters and annual income in dollars, it has been determined that for Group 1, r2 =0.15 and for Group 2, r2 =0.10 where r denotes the
A. There could be a positive relationship between the two variables for Group 1 and a negative relationship between the two variables for Group 2
B. The sum of the residuals for Group 1 is greater than the sum of the residuals for Group 2.
C. Measuring the height in inches would increase the value of r2 for both groups.
D. None of the answer options is true
Can you also explain the difference between r and r2, and why least square regressions are used?
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