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difference between correlation and regression?
(1) The correlation answers the STRENGTH of linear association between paired variables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X.
(2a) Correlation is calculated whenever:
* both X and Y is measured in each subject and quantify how much they are linearly associated.
* in particular the Pearson's product moment correlation coefficient is used when the assumption of both X and Y are sampled from normally-distributed populations are satisfied
* or the Spearman's moment order correlation coefficient is used if the assumption of normality is not satisfied.
* correlation is not used when the variables are manipulated, for example, in experiments.
(2b) Linear regression is used whenever:
* at least one of the independent variables (Xi's) is to predict the dependent variable Y. Note: Some of the Xi's are dummy variables, i.e. Xi = 0 or 1, which are used to code some nominal variables.
* if one manipulates the X variable, e.g. in an experiment.
(3) Linear regression are not symmetric in terms of X and Y. That is interchanging X and Y will give a different regression model (i.e. X in terms of Y) against the original Y in terms of X.
On the other hand, if you interchange variables X and Y in the calculation of correlation coefficient you will get the same value of this correlation coefficient.
(4) The "best" linear regression model is obtained by selecting the variables (X's) with at least strong correlation to Y, i.e. >= 0.80 or <= -0.80
(5) The same underlying distribution is assumed for all variables in linear regression. Thus, linear regression will underestimate the correlation of the independent and dependent when they (X's and Y) come from different underlying distributions.
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ReneRegression coefficient measures the change in the dependent variable for a one-unit change in the independent variable, while correlation coefficient measures the strength and direction of the linear relationship between two variables. Regression coefficient is specific to the relationship between two variables in a regression model, while correlation coefficient is a general measure of association between two variables.
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What is the difference between a subscript and a coefficient in a chemical formula?
The subscripts tell you how the atoms are bound together. The coefficient tells you how many atoms there are.
What does the science symbol r mean?
In science, the symbol "r" typically refers to the correlation coefficient, which measures the strength and direction of a relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.
Measure of how closely one thing is related to another?
This is referred to as correlation, which quantifies the strength and direction of the relationship between two variables. The correlation coefficient can range from -1 to 1, where values closer to 1 indicate a strong positive relationship, values close to -1 indicate a strong negative relationship, and a value of 0 indicates no relationship.
What kind of test used to analyze data for experimental treatments?
After calculating the mean and standard deviationvalues each value of the independent variable in the data, these are a few common tests that are used to further analyse the data and highlight its significance:1) Pearson Correlation Coefficient- This is to test for a strong/weak positive/negative correlation between the independent variable and the dependent variable. However, correlation does not necessarily imply causation.2) t-test- This post-hoc test is used to determine the level of significance of the difference between two sets of data.3) Chi2 test- This test tests for whether the difference in Expected and Observed values are significant or not.4) Analysis of variance (ANOVA)- This is like a massive t-test to test an entire set of data, without inflating the error of the analysis results. This is usually coupled with Tukey's Honest Significant Difference test.
What is a Pearson correlation and an example of it?
A Pearson correlation measures the strength and direction of a linear relationship between two continuous variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation). An example could be studying the correlation between the amount of rainfall and crop yield in agricultural research to understand how variations in rainfall affect crop productivity.
