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.

Answer 2

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.

Given :-

• Initially R-Squared = 12.78%

• As the math score increases by 1 point on average the verbal            score increases by 12.78 points and vice versa

According to the statement, we first understand what is Correlation coefficient.

What is Correlation coefficient?

The correlation coefficient is a "Statistical measurement" which calculates the strength of the relationship b/w the Relative movements of two the variables". Denoted by r and its range lies between (-1 , 1).

In order to find the Correlation coefficient,we will use this formula:-

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

 

Now, we use the value for representing the determination coefficient which is useful  for find the percentage of variability which will explained by The linear mode.

Here According to the survey they want to find the verbal score based on the math score (independent variable).

• Verbal score = Dependent variable.
• Mathematics score = Independent variable.

We know that,

                               $\longrightarrow\rm r^{2} =0.1278\\\longrightarrow \rm r=\sqrt{0.1278}$

Now,We will analyze one by one for given statements:-

Statement(1):- 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

TRUE, Because of verbal and maths score and 12.78% of variability is            explained by the given model.

Statement(2):- 12.78% of the variability of math score that can be explained by the linear regression on the verbal score.

FALSE,Because Verbal score is our dependent variable not the math score.

Statement(3):- As the math score increases by 1 point on average, the verbal score increases by 12.78 points.

FALSE, the slope of a linear model is not represented by  Determination coefficient .

Statement (4):- As the verbal score increases by 1 point on average, the math score increases by 12.78 points.

FALSE, the slope of a linear model is not represented by  Determination coefficient.

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