Use the following information for questions:
A graduate student is doing a research project on stress among recent immigrants. She focused on parents of young children. All parents answered questions on a questionnaire (with the help of a translator if necessary). A stress score was calculated for all participants. SPSS was used to run a simple linear regression in which y = stress of the parent and x = age of the parent.

-A least squares line or least squares regression line has the property that the sum of squared differences between the observed values of y and the predicted values $\hat{y}$ is smaller for that line than it is for any other line. What is the value of the SSE for this regression line?
A) 0.257
B) 14.354
C) 14.611
D) 0.422

Question

Use the following information for questions:
 A graduate student is doing a research project on stress among recent immigrants. She focused on parents of young children. All parents answered questions on a questionnaire (with the help of a translator if necessary). A stress score was calculated for all participants. SPSS was used to run a simple linear regression in which y = stress of the parent and x = age of the parent.
  
-A least squares line or least squares regression line has the property that the sum of squared differences between the observed values of y and the predicted values $\hat{y}$ is smaller for that line than it is for any other line. What is the value of the SSE for this regression line?
A) 0.257 
B) 14.354 
C) 14.611 
D) 0.422

Quizplus · Accepted Answer

The Sum of Squared Errors (SSE) for the least squares regression line is minimized compared to any other line, but it is not necessarily close to zero unless the data points perfectly fit the line. Among the provided options, 14.354 (B) is a plausible value for SSE, indicating some level of error between the observed values and the predicted values on the regression line.

Use the Following Information for Questions: a Graduate Student y^\hat{y}y^​

Use the Following Information for Questions:
a Graduate Student $\hat{y}$