Which of these correlation numbers shows the strongest relationship? | Socratic
a graphical representation that includes both of these variables. Such a graphical representation is called a scatterplot. A scatterplot shows the relationship between two quantitative variables . The strongest linear relationship occurs when the slope is 1. A correlation coefficient measures the strength of that relationship. Which of the following correlation coefficients indicates the strongest relationship between variables The closer to either extreme, the stronger the relationship. The sign of the correlation coefficient indicates the direction of the association. . For either of these relationships we could use simple linear regression analysis Based on the observed data, the best estimate of a linear relationship will be.
The larger the absolute value of the coefficient, the stronger the relationship between the variables.
For the Pearson correlation, an absolute value of 1 indicates a perfect linear relationship. A correlation close to 0 indicates no linear relationship between the variables.
Which of these correlation numbers shows the strongest relationship?
Direction The sign of the coefficient indicates the direction of the relationship. If both variables tend to increase or decrease together, the coefficient is positive, and the line that represents the correlation slopes upward. If one variable tends to increase as the other decreases, the coefficient is negative, and the line that represents the correlation slopes downward. The following plots show data with specific correlation values to illustrate different patterns in the strength and direction of the relationships between variables.
The covariance of gestational age and birth weight is: Finally, we can ow compute the sample correlation coefficient: Not surprisingly, the sample correlation coefficient indicates a strong positive correlation.
In practice, meaningful correlations i. There are also statistical tests to determine whether an observed correlation is statistically significant or not i.
- Simple Linear Regression
- Example - Correlation of Gestational Age and Birth Weight
- Step 1: Examine the linear relationship between variables (Pearson)
Procedures to test whether an observed sample correlation is suggestive of a statistically significant correlation are described in detail in Kleinbaum, Kupper and Muller. We introduce the technique here and expand on its uses in subsequent modules.
Simple Linear Regression Simple linear regression is a technique that is appropriate to understand the association between one independent or predictor variable and one continuous dependent or outcome variable. In regression analysis, the dependent variable is denoted Y and the independent variable is denoted X. The measures of association, gamma and the coefficient of contingency, provide an index of the strength of the relationship. When we have two interval level variables, it is awkward to put them into a crosstab, because there are too many levels of each variable.
Interpret the key results for Correlation - Minitab Express
Still, it would be useful to have a measure of association and a significance test for hypotheses about interval level variables. The Pearson correlation coefficient is an index of the strength and direction of a linear relationship between two interval level variables.
The Scatterplot The best way to understand the concept of correlation is to visualize it. We can depict the relationship between two interval level variables in a scatterplot. Imagine what the scatterplot would look like if there is no relationship between two variables: It looks like a random cloud of points. The correlation for this data is 0.
Now, imagine what the scatterplot would look like if there is a very strong relationship between two variables: All the points align along a straight line. The correlation for this data is 1. This is a perfect positive correlation. If the data were perfectly related, in the negative direction, the scatterplot would look like: The Strength of the Relationship The magnitude of the correlation coefficient tells us how close the relationship is to the ideal cases: If the coefficient is near zero, the relationship is weak.
In fact, we would say that there is no relationship between the variables. If the coefficient is near 1. The correlation coefficient is 0. This is a weak positive relationship.
This scatterplot depicts the relationship between the Number of Sports Events and the Number of Museums for the same cities: This is a moderate positive relationship. This scatterplot depicts the relationship between the Number of Authors and the Number of Musicians for these cities: