Question

3. Lori created a scatterplot where the explanatory variable was the side of a square, and the response variable was the perimeter of the square. Is the data positively or negatively correlated? Explain.

Answer 1

Positively Correlated

Explanation:

The variable that we can change is called the Explanatory variable.

The response variable depends upon the explanatory variable, as we change the value of the explanatory variable the value of the response variable is also get changed.

Correlation shows the strength of the relation between two variables.

Correlation is said to be positive correlation if increasing/decreasing the explanatory variable, also increases/decreases the values of the response variable.

Correlation is said to be negative correlation if increasing/decreasing the explanatory variable, also decreases/increases the values of the response variable.

We know that,

Perimeter = 4 × (Sides of Square)

Here it is given that "Perimeter" is the Response variable.

and "Side of Square" is the explanatory variable.

As we increase the value of Sides of Perimeter, the value of Perimeter is increase four times.

Hence, data is positively correlated.

Answer 2

We want to determine if side of a square and its perimeter are positively correlated

Let the side of the square be 'a' units.

Then, the perimeter of the square would be = 4×a units

Hence, we can see that for each unit increase in 'a', the perimeter would increase 4 times.

Hence, both the side and the perimeter are moving in the same direction. Hence, they are positively correlated