# What correlation coefficient represents the strongest relationship

### Correlation Review and Practice Exercises

The Pearson correlation coefficient is an index of the strength and direction of a The sign of the correlation coefficient indicates the direction of the relationship. Correlation coefficient: Indicates the direction, positively or negatively of the relationship, and how strongly the 2 variables are related. Which of the following sequences of correlation coefficients correctly arranges the relationships between three pairs of two variables in order of increasing.

It's going to approach this thing here. If we look at our choices, it wouldn't be r equals 0. These are positive so I wouldn't use that one or that one. And this one is almost no correlation. R equals negative 0. I feel good with r is equal to negative 0. I wanna be clear, if I didn't have these choices here, I wouldn't just be able to say, just looking at these data points without being able to do a calculation, that r is equals to negative 0.

I'm just basing it on the intuition that it is a negative correlation, it seems pretty strong. The pattern kind of jumps out at you, that when y is large, x is small.

**Linear relationship and the correlation coefficient (KC)**

When x is large, y is small. So I like something that's approaching r equals negative one. I've used this one up already. Now scatterplot B, if I were to just try to eyeball it, once again this is gonna be imperfect. But the trend, if I were to try to fit a line, it looks something like that.

### Statistics 2 - Correlation Coefficient and Coefficient of Determination

It looks like a line fits in reasonably well. There's some points that would still be hard to fit. They're still pretty far from the line. It looks like it's a positive correlation.

## Example: Correlation coefficient intuition

When y is small, x is relatively small and vice versa. As x grows, y grows and when y grows, x grows. This ones going to be positive and it looks like it would be reasonably positive.

I have two choices here. I don't know which of these it's going to be. It's either going to be r is equal to 0. I also got scatterplot C, this ones all over the place.

It kinda looks like what we did over here. What does a line look like? You could almost imagine anything. Does it look like that? Does a line look like that? There's not a direction that you could say, "Well, as x increases, maybe y increases or decreases. So this one is pretty close to zero.

I feel pretty good that this is the r is equal to negative. In fact, if we tried probably the best line that could be fit, would be one with a slight negative slope. It might look something like this. And notice, even when we try to fit a line, there's all sorts of points that are way off the line. So the linear model did not fit it that well. R is equal to negative 0. Now we have scatterplot D. That's gonna use one of the other positive correlations and it does look like there is a positive correlation.

When y is low, x is low. When x is high, y is high and vice versa. We could try to fit something that looks something like that. But it's still not as good as that one. You can see the points that we're trying to fit, there's several points that are still pretty far away from our model. The model is not fitting it that well, so I would say scatterplot B is a better fit.

A linear model works better for scatterplot B than it works for scatterplot D. I would give the higher r to scatterplot B and the lower r, r equals 0. This is a weak positive relationship. This scatterplot depicts the relationship between the Number of Sports Events and the Number of Museums for the same cities: This is a moderate positive relationship.

This scatterplot depicts the relationship between the Number of Authors and the Number of Musicians for these cities: This is a strong positive relationship; the correlation coefficient is 0. The Direction of the Relationship The sign of the correlation coefficient indicates the direction of the relationship. A positive relationship means that larger scores on one variable are associated with larger scores the other variable.

A negative, or inverse, relationship means that larger scores on one variable are associated with smaller scores on the other variable.

### Which of these correlation numbers shows the strongest relationship? | Socratic

Interpreting the Correlation Coefficient There is no rule for determining what size of correlation is considered strong, moderate or weak. The interpretation of the coefficient depends, in part, on the topic of study. When we are studying things that are difficult to measure, such as the contents of someone's mental life, we should expect the correlation coefficients to be lower. In these kinds of studies, we rarely see correlations above 0.

For this kind of data, we generally consider correlations above 0. When we are studying things that are more easily countable, we expect higher correlations. For example, with demographic data, we we generally consider correlations above 0. One useful way to interpret the correlation coefficient is based on explained variation. The square of the correlation coefficient is equal to the proportion of variation in the dependent variable that is accounted for, or explained, by variation in the independent variable.

A correlation of 0. The Significance Test If we collect data from a random sample, and calculate the correlation coefficient for two variables, we need to know how reliable the result is. This calls for a statistical test.

Let's say we have collected data on U. We want to know if there is a relationship between the number of artists in a community and the amount of arts funding it received. Start, as always, with the hypotheses. The null hypothesis states that there is no linear relationship between the independent variable and the dependent variable. In our example, the null hypothesis is that there is no relationship between the number of artists in a community and the amount of grant funding it received.

Next, we calculate the correlation coefficient for the sample. As always, if the significance, p, is less than or equal to 0. We can reject the null hypothesis and interpret the correlation coefficient. The number of artists in a community is positively related to the amount of grant funding it received. Communities with more artists tended to receive more grant funding.

## Which of these correlation numbers shows the strongest relationship?

Partial Correlations Based on the data from our sample, we concluded that there is a positive relationship between number of artists and amount of grant funding. We assumed that the number of artists in a community is the causal factor, or, in other words, that the presence of more artists in the community leads to more grant funding. This makes logical sense: We must be careful in our interpretation, however.