Question

A survey of Statistics undergraduate at Prosperity University completed a survey that asked for their Verbal and Math SAT scores. They wanted to predict the verbal score based on the math score. The value of R-Squared was 12.78%. Interpret R-squared. Group of answer choices 12.78% of the variability of verbal score that can be explained by the linear regression on the math score. 12.78% of the variability of math score that can be explained by the linear regression on the verbal score. As the math score increases by 1 point on average, the verbal score increases by 12.78 points. As the verbal score increases by 1 point on average, the math score increases by 12.78 points.
Group of answer choices

12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

12.78% of the variability of math score that can be explained by the linear regression on the verbal score.

As the math score increases by 1 point on average, the verbal score increases by 12.78 points.

As the verbal score increases by 1 point on average, the math score increases by 12.78 points.

Answer 1

Answer:

12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

Correct, as we can see our dependent variable is the verbal score and the independnet variable is the math score and 12.78% of the variability is explained by the model.

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$  

The value for $r^2$ represent the determination coefficient and is useful in order to find the % of variability explained by a linear model

Solution to the problem

For this case they wanted to predict the verbal score (dependent variable) based on the math score (independent variable).

For this case we know that $r^2 = 0.1278$

So then $r= \sqrt{0.1278}=0.357$

Let's analyze one by one the possible options for this case:

12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

Correct, as we can see our dependent variable is the verbal score and the independnet variable is the math score and 12.78% of the variability is explained by the model.

12.78% of the variability of math score that can be explained by the linear regression on the verbal score.

False, our dependent variable is the verbal score not the math score.

As the math score increases by 1 point on average, the verbal score increases by 12.78 points.

False, the determination coefficient not represent the slope for a linear model.

As the verbal score increases by 1 point on average, the math score increases by 12.78 points.

False, the determination coefficient not represent the slope for a linear model.