Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm) . The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.
-What is the value of r², the proportion of variation in left hand spans explained by the linear relationship with right hand spans.

Question

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm) . The least squares regression equation is

\hat{y}

= 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.
-What is the value of r², the proportion of variation in left hand spans explained by the linear relationship with right hand spans.

Quizplus · Accepted Answer

The proportion of variation in left hand spans explained by the linear relationship with right hand spans is calculated using the coefficient of determination, $R^2$, which is given by $R^2 = 1 - \frac{SSE}{SSTO}$. Substituting the given values, $R^2 = 1 - \frac{76.67}{784.8}$, which calculates to approximately 0.902 or 90.2%.

Use the Following Information for Questions: a Representative Sample y^\hat{y}y^​

Use the Following Information for Questions:
a Representative Sample $\hat{y}$