How can one use the value of r to determine whether or not two continuous variables are linear?
To give a siple answer: yes, it is possible to show a correlation between two variables.
Having a high value like e.g. +1 shows that the two variable have the same tendency to increase -> meansing that var1 has higher values when var2 also shows higher values
Nevertheless, using the correlation coefficient alone is never advisable. There are correlations that lead to high correlation although variables have no linear relationsship.
One of the easiest ways is to have look at your scatterplot (as long as there are enough data). Many statistical values just make sense when the amount of data points is high enough. It is not pretty to construct something linear having yust a few points.
Please refer to the famous data set created with Francis Anscombe: https://en.wikipedia.org/wiki/Anscombe%27s_quartet
Jan
Yes, the correlation coefficient can also be used to determine whether there is a linear relationship between two variables. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. If the correlation coefficient is close to -1 or 1, it indicates a strong linear relationship, whereas if it is close to 0, it indicates a weak or no linear relationship. It is important to note that a high correlation coefficient does not necessarily mean that there is a causal relationship between the two variables, and there may be other factors involved. Therefore, it is important to use caution when interpreting correlation coefficients and to consider other information and analysis methods as well.
The value of r, the correlation coefficient, can be used to determine whether or not two continuous variables are linear. The Pearson correlation coefficient, r, ranges from +1 to -1, with values close to 1 indicating a strong positive linear relationship, values close to -1 indicating a strong negative linear relationship, and values close to 0 indicating little or no linear relationship. Therefore, a higher absolute value of r indicates a stronger linear relationship between the two variables. It is important to note that correlation does not imply causation, and other factors may be involved in the relationship between the variables. Also, it is important to use other analysis methods and consider other information as well when interpreting correlation coefficients.
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