Question

The following table lists the birth weight (in pounds), x, and the lengths (in inches),y, for a set of newborn babies at a local hospital.  

Birth Weight (in pounds), x	5	3	8	6	9	7	7	6	6	10
Length(in inches),y	16	15	18	19	19	18	20	17	15	21

Enter this information on your calculator and then answer the following:

(A) What kind of linear relationship seems to exist between birth weights of newborn babies and their lengths?

(B) Calculate the correlation coefficient, r ?

(C) Determine the equation of the line of best fit.

(D) Calculate and interpret the coefficient of determination , r ² .

(E) Make a scatter plot of data.

(F) Predict the length of an 4-pound baby.

Answer 1

	Birth weight (X)	Length (Y)	X * Y
	5	16	80	25	256
	3	15	45	9	225
	8	18	144	64	324
	6	19	114	36	361
	9	19	171	81	361
	7	18	126	49	324
	7	20	140	49	400
	6	17	102	36	289
	6	15	90	36	225
	10	21	210	100	441
Total	67	178	1222	485	3206

There is positive and strong relationship between variables.

r = 0.798

Equation of regression line is


b = 0.814

a =( 178 - ( 0.8144 * 67 ) ) / 10
a = 12.343
Equation of regression line becomes

Coefficient of Determination

Explained variation = 0.637* 100 = 63.7%
Unexplained variation = 1 - 0.637* 100 = 36.3%

When X = 4
= 12.343 + 0.814 X
= 12.343 + 0.814 * 4
= 15.6