Asked by Shanna Daniels on Jun 07, 2024
Verified
In a simple linear regression problem, the following sum of squares are produced: . The percentage of the variation in y that is explained by the variation in x is:
A) 25%
B) 75%
C) 33%
D) 50%
E) 150%
Sum Of Squares
The sum of the squared differences between each observation and the overall mean, used in various statistical methods.
- Describe the link between the coefficient of correlation and the coefficient of determination.
Verified Answer
CB
Calvin BakhtiyarovJun 13, 2024
Final Answer :
B
Explanation :
The percentage of variation in y that is explained by the variation in x is given by the coefficient of determination, which is the ratio of the explained variation to the total variation. The explained variation is the sum of squares of regression (SSR), and the total variation is the sum of squares total (SST). Therefore, the coefficient of determination is:
$R^2 = SSR/SST = (SST - SSE)/SST = 1 - SSE/SST$
where SSE is the sum of squares error.
Since only the SSR is given in the problem, we cannot directly calculate R^2. However, we do know that SSE + SSR = SST. Therefore, we can calculate SSE by subtracting SSR from SST:
SSE = SST - SSR =
Now we can calculate R^2:
$R^2 = 1 - SSE/SST = 1 - 11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_12 /11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_11 = 0.75$
Therefore, the percentage of variation in y that is explained by the variation in x is 75%, which corresponds to choice B.
$R^2 = SSR/SST = (SST - SSE)/SST = 1 - SSE/SST$
where SSE is the sum of squares error.
Since only the SSR is given in the problem, we cannot directly calculate R^2. However, we do know that SSE + SSR = SST. Therefore, we can calculate SSE by subtracting SSR from SST:
SSE = SST - SSR =
Now we can calculate R^2:
$R^2 = 1 - SSE/SST = 1 - 11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_12 /11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_11 = 0.75$
Therefore, the percentage of variation in y that is explained by the variation in x is 75%, which corresponds to choice B.
Learning Objectives
- Describe the link between the coefficient of correlation and the coefficient of determination.
Related questions
If the Coefficient of Correlation Is 1 ...
Given the Least Squares Regression Line ,And a Coefficient ...
If the Coefficient of Determination Is a Positive Value, Then ...
In a Regression Analysis, the Regression Equation Is Given by ...
When Computing the Correlation Coefficient,the ______ Between Variables,not the ______ ...