Respuesta :
Answer:
I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between minus 1 and 1.
Step-by-step explanation:
A correlation coefficient is a measure of how closely the variables are related. This coefficient ranges from -1 to 1, with -1 being a perfect fit for a decreasing data set and 1 being a perfect fit for an increasing data set.
If the data set has a negative correlation coefficient, the data is decreasing; this means that the slope of the regression line will be negative.
The closer the correlation coefficient is to -1 or 1, the better the fit; this means that a correlation coefficient of -0.82 will be stronger than one of 0.62.
The statements that are true concerning a linear correlation coefficient are: I, II, and III.
Recall:
- Linear correlation coefficient, r, is a value that ranges between -1 to 1.
- The value of a linear correlation coefficient shows whether the strength of correlation between two variables.
- Correlation coefficient, r, of zero shows no correlation between two variables, while the closer the correlation coefficient value is to 1 or -1, the stronger the relationship between the two variables that are correlated.
- A graph that has a negative slope will have a linear correlation coefficient that is negative.
Considering the above stated facts, the statements that are true concerning a linear correlation coefficient are: I, II, and III.
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