Ascatterplot containing several values is found to have a linear regression r2 value of 0.883, a quadratic regression r2 value of 0.537, an exponential regression r2 value of 0.492, and a logarithmic regression r2 value of 0.912. which mathematical model best fits the scatterplot?

the mathematical model that best fits the scatterplot is the logarithmic regression with r² = 0.912.

Explanation:

1) The regression model is a curve that tries to adjust the given points and to estimate other points.

2) The curve, in general does not adjust perfectly. This is, when you use the equation of the model, the y-values that you obtain for any input (x-values) are different from the real data.

3) The statistical r² measures the average differences between the data and the model.

An r² equal to 1 would be a perfect match. This is, the equation of the model would reproduce the data perfectly.

So, 1 is the maximum possible value for r².

In the measure that the model is not a good fit, r² decreases (it can never be 0.

So, r² is in the interval (0, 1], and the closer to 1 the better the model represent the data.

3) Since the logarithmic regression r² value is the closest to 1 among all the models reported, that is the one that best fits the scatterplot.

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.