Answer to Suppose that the relationship between price, P, and quantity,, is given by the eqion P Which of the following equat. Answer to Suppose a relationship between two variables is found to be statistically significant. Explain whether each of the follo. CA needs to remove all parameters corresponding to SC. Revoking an Existing Relationship Suppose the relationship between two immediate security.

So let's draw that. The slope seems to be positive, although it's not as positive as it was there. So the slope looks like it is-- I'm just trying to eyeball it-- so the slope is a constant positive this entire time.

We have a line with a constant positive slope. So it might look something like this. And let me make it clear what interval I am talking about. I want these things to match up.

### The graphical relationship between a function & its derivative (part 1) (video) | Khan Academy

So let me do my best. So this matches up to that. This matches up over here. And we just said we have a constant positive slope. So let's say it looks something like that over this interval. And then we look at this point right over here.

So right at this point, our slope is going to be undefined. There's no way that you could find the slope over-- or this point of discontinuity. But then when we go over here, even though the value of our function has gone down, we still have a constant positive slope.

### Is side length & area proportional? (video) | Khan Academy

In fact, the slope of this line looks identical to the slope of this line. Let me do that in a different color. The slope of this line looks identical.

So we're going to continue at that same slope. It was undefined at that point, but we're going to continue at that same slope.

And once again, it's undefined here at this point of discontinuity. So the slope will look something like that. And then we go up here. The value of the function goes up, but now the function is flat. So the slope over that interval is 0.

The slope over this interval, right over here, is 0.

So we could say-- let me make it clear what interval I'm talking about-- the slope over this interval is 0. And then finally, in this last section-- let me do this in orange-- the slope becomes negative.

## Linear, nonlinear, and monotonic relationships

But it's a constant negative. And it seems actually a little bit more negative than these were positive. So I would draw it right over there. So it's a weird looking function. Weak linear relationship Plot 4: Nonlinear relationship The data points in Plot 3 appear to be randomly distributed.

## The graphical relationship between a function & its derivative (part 1)

They do not fall close to the line indicating a very weak relationship if one exists. If a relationship between two variables is not linear, the rate of increase or decrease can change as one variable changes, causing a "curved pattern" in the data.

This curved trend might be better modeled by a nonlinear function, such as a quadratic or cubic function, or be transformed to make it linear. Plot 4 shows a strong relationship between two variables.

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This relationship illustrates why it is important to plot the data in order to explore any relationships that might exist. Monotonic relationship In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. In a linear relationship, the variables move in the same direction at a constant rate. Plot 5 shows both variables increasing concurrently, but not at the same rate.

This relationship is monotonic, but not linear. The Pearson correlation coefficient for these data is 0. Linear relationships are also monotonic.