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# 统计代写|统计入门代写Introduction to Statistics代考|KMA153 What Is the Most Direct Way to Interpret the Value of a Correlation Coefficient?

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## 统计代写|统计入门代写Introduction to Statistics代考|What Is the Most Direct Way to Interpret the Value of a Correlation Coefficient?

The correlation coefficient is a numerical value that indicates the degree of relationship between two variables. The value of any correlation coefficient ranges from $-1.00$ (a perfectly indirect or negative correlation) to $+1.00$ (a perfectly direct or positive correlation). But how does one interpret this value? What does it mean?

The most direct way to interpret a correlation coefficient is to use the following table. This will give you a quick assessment of the strength of the correlation.

While using the above table is not the most precise way of interpreting the strength of a correlation coefficient, it certainly provides a sense of the strength of the relationship between variables. For a more precise method, we’ll turn to question $# 47$, which deals with the coefficient of determination.

## 统计代写|统计入门代写Introduction to Statistics代考|What Is the Coefficient of Determination, and How Is It Computed?

Ithough a simple examination of the value of a correlation coefficient can provide a general assessment of the strength of the relationship between two variables, there is a far more precise way to do this.

The coefficient of determination, represented as $r_{x y}{ }^2$ or the square of the correlation coefficient, yields the amount of variance in one variable that is accounted for by changes in another variable. The concept of the coefficient of determination is based on the fact that variables that are correlated with one another share something in common. The stronger the relationship $\left(r_{x y}\right)$, the more they share and the higher the coefficient of determination.

For example, let’s take the correlation between height and weight for a class of sixth graders, which is found to be 85 . Thus, the simple Pearson product-moment correlation or $r_{x y}=.85$. The coefficient of determination is $.7225$, which means that $72.25 \%$ of the variance in height (how much sixth graders differ from each other in height) can be accounted for by the variance in weight (how much sixth graders differ from each in weight).
There are several important things to remember about the use of this coefficient.

The first is that the stronger the simple correlation, the more variance is accounted for. For example, if the correlation between one variable and the other is $.4$, then only 16 or $16 \%$ of the variance in one is accounted for by the relationship between variables. If the correlation between one variable and another is $.6$, then $.36$ or $36 \%$ of the variance is accounted for.
The second (related to the first) is that the more that one variable has in common with a second variable (and the stronger the correlation), the larger the coefficient of determination will be.

If there is no relationship between variables (when $r_{x y}=0$ ), then nothing is shared between the two variables, and no variance or change in one can be accounted for by a change in the other.

Indirect or negative correlations, which have a negative sign (such as $-.13$ or $-.87$ ) are neither “better” nor “worse” than direct or positive correlation coefficients-just very different.

A correlation always reflects a situation in which there are at least two data points (or variables) per case.

A correlation indicates nothing about the causal relationship between variables; it reflects only the strength of their association.

Scatter charts are the best choice to display the visual relationship between points whose correlation is being explored.

## 统计代写|统计入门代写INTRODUCTION TO STATISTICS代 考|WHAT IS THE COEFFICIENT OF DETERMINATION, AND HOW IS IT COMPUTED?

$72.25 \%$ 高度的变化howmuchsixthyradersdifferfromeachotherinheight可以通过重量的变化来解释howmuchsixthgradersdiffer fromeachinweight.

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