The error in the conclusion of "cigarettes cause the pulse rate to increase" is that it cannot be concluded that cigarettes "cause" the pulse rate to increase.
Linear correlations measure the association and strength between two variables. Correlations refer to the interdependence or co-relationships between the variables.
It reflects the closeness between the x variable which is the independent variable called the predictor and the y variable is the dependent variable, also known as the outcome.
The correlation can be determined through using the simple linear regression. This is a procedure that provides an estimate of the value of the outcome based on the predictor.
The use of linear correlation and regression is to test the hypothesis of cause and effect, to see whether the two variables are associated and to estimate the value of one variable corresponding to a particular value of the other variable.
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