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.
-Use the empirical rule to find an interval that describes the left hand spans of approximately 95% of all individuals who have a right hand span of 26 cm.
A) (23.12, 25.66)
B) (24.57, 27.12)
C) (28.33, 30.87)
D) None of the above

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.
-Use the empirical rule to find an interval that describes the left hand spans of approximately 95% of all individuals who have a right hand span of 26 cm.
A) (23.12, 25.66)
B) (24.57, 27.12)
C) (28.33, 30.87)
D) None of the above

Quizplus · Accepted Answer

The predicted left hand span for a right hand span of 26 cm is $\hat{y} = 1.46 + 0.938 \times 26 = 25.828$. The standard error of the estimate is $\sqrt{SSE/(n-2)} = \sqrt{76.67/188} \approx 0.637$. Using the empirical rule, approximately 95% of values lie within 2 standard deviations, so the interval is $25.828 \pm 2 \times 0.637 = (24.57, 27.12)$.

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

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