Question

The heights of five female students and their mothers in inches are provided Using these values, complete parts (a) through (e) below PH Click the icon to view the heights (a) Figure the correlation coefficient (Round to two decimal places as needed) (b) Determine the score prediction model for predicting a female student's height from her mother's height i Heights Student Mother's Height Student's Height Predicted Zy (Predicted Zx) (Round to two decimal places as needed) (c) Based on the prediction model, predict the height of a female student whose mother's height is 5 feet The predicted height is inches. (Round to two decimal places as needed) (d) Based on the prediction model predict the height of a female student whose mother's height is 5 feet 6 inches The predicted height is inches Round to two decimal places as needed) Print Done Enter your answer in each of the answer boxes

Answer 1

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
0	-2.4	0	0
2	3.6	4	7.2
-1	-6.4	1	6.4
5	5.6	25	28
-6	-0.4	36	2.4

SS: Total of (X - M_x)²

= 66

SP: Total of  (X - M_x)(Y - M_y)

= 44

Sum of X = 315
Sum of Y = 322
Mean X = 63
Mean Y = 64.4
Sum of squares (SS_X) = 66
Sum of products (SP) = 44

b = SP/SS_X = 44/66 = 0.66667

a = M_Y - bM_X = 64.4 - (0.67*63) = 22.4

ŷ = 0.66667X + 22.4

c) Mother's Height = 5ft

ŷ = 0.66667X + 22.4

= 0.66667 (5) + 22.4

= 25.74

The predicted height is 25.74 inches

d) Mother Height = 5.6

ŷ = 0.66667X + 22.4

= 0.66667 (5.6) + 22.4

= 26.14

The predicted height is 26.14 inches