Finite Math Help: Similarities, Correlation Coefficient & Determination

[tofu]

have some questions

first, i would like to know what are the similarities and differences for the above terms..

also, a correlation coefficient ranges from -1 to 1 while correlation determination ranges from 0 to 1,

why can't the correlation determination be negative?
what can't the correlation coefiicient be over 1?

 

[cookiemonster]

And the "above terms" are...?

r may range from -1 to 1, but when you square it, then negative goes away. $(-.5)^2 = .25$.

cookiemonster

 

[M98Ranger]

The terms similarities, correlation coefficient, and determination all relate to the concept of measuring the strength and direction of a relationship between two variables. They are often used in statistics and mathematics to analyze data and make predictions.

Similarities:
1. Both correlation coefficient and determination are measures of the strength of a relationship between two variables.
2. They both range from 0 to 1.
3. They are both used to determine the degree of linear relationship between two variables.

Differences:
1. Correlation coefficient measures the strength and direction of a linear relationship between two variables, while determination measures the proportion of variance in one variable that is explained by the other variable.
2. Correlation coefficient can range from -1 to 1, while determination can only range from 0 to 1.
3. Correlation coefficient can be positive, negative, or zero, while determination can only be positive.
4. Correlation coefficient is affected by the units of measurement of the variables, while determination is not.

The correlation coefficient ranges from -1 to 1 because it measures the strength and direction of a linear relationship. A negative correlation coefficient indicates a negative relationship, meaning that as one variable increases, the other decreases. Similarly, a positive correlation coefficient indicates a positive relationship, meaning that as one variable increases, the other also increases. A correlation coefficient of 0 indicates no linear relationship between the two variables.

On the other hand, determination can only range from 0 to 1 because it measures the proportion of variance in one variable that is explained by the other variable. A determination of 0 means that the two variables have no linear relationship, while a determination of 1 means that all of the variance in one variable can be explained by the other variable.

The correlation determination cannot be negative because it measures the proportion of variance in one variable that is explained by the other variable. A negative determination would mean that the variance in one variable is explained by the other variable in a negative way, which does not make sense.

Similarly, the correlation coefficient cannot be over 1 because it measures the strength of a linear relationship between two variables. A correlation coefficient of over 1 would mean that there is a stronger linear relationship than is physically possible.