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# Bivariate relationship linearity, strength and direction

Describe a bivariate relationship's linearity, strength, and direction.

## Want to join the conversation?

• Is a rectangular hyperbola (y = 1/x) classified as a negative non-linear relationship? The curve Sal draws in the tutorial is very much like a rectangular hyperbola (y = 1/x), but the equation, unlike y = -x + k (a negative linear relationship), doesn't have a negative sign. So, how do you classify a hyperbolic relationship of the forms like y = 1/x, y = 1/x^2, and the like?
• Negative just means that as one variable increases, the other decreases. You're right that the curve could be considered y = 1/x, in which case, as x get larger, y gets smaller, thus there is a negative relationship.
(1 vote)
• Sometimes, wouldn't it just also be your opinion on if it's linear or non-linear if its not completely clear? For example at , he said the graph was linear but it looked kind of non-linear to me.
• You are right that an exercise like this gives quite some room for personal interpretation, and at the end of the video Sal mentions this.
• can you have a scatter plot graph that is straight up and down?
• I suppose you could if one variable of the equation is in a set group variability, but generally a scatter plot does not have any set variables. But if a scatter plot goes straight up and down where all of the points have the same x coordinate, this would mean that all of the points are in a single fine line with no variation, then you cant really consider that a scatter plot. At that point is just a line. But if there is some variation of the points, them being spread out a little, Then yes that is a scatter plot.
• what is the meaning about direction?
• The negative slope is decreasing and the positive slope is increasing.
• How do you know the graph is strong or not.
• If the value of r is high close to 1 or -1 then you know there is a strong relationship between the two variables. Generally, if it is greater than .7 it is "strong".
• What are the characteristics of bivariate data that shows a linear and non-linear relationship in a graph?
• It's all about what type of function best fits the data. If a straight line looks like the best fit for the relationship between two variables then the relationship is linear. If a curved line would fit the relationship best, then the relationship is non-linear (perhaps parabolic as in y=x^2, or some other non-linear functional form).

I hope that helps!
• I'm confused, how am I supposed to determine a graph's strength?
• You should look at the correlation coefficient, R. If r is close to 1 or -1 is said to be strong.