Question

A study on the relationship between the estriol levels of pregnant women and the birth weights of their children is given in the table.​ Here, x denotes estriol​ level, in​ mg/24 hr, and y denotes birth​ weight, in hectograms. Use the information to complete parts​ (a) through​ (d).
x: 15, 25, 21, 18, 27, 12, 19, 16
y: 33, 39, 34, 33, 44, 25, 35, 32

(a) Decide whether finding a regression line for the data is reasonable. If​ so, then also do parts ​(b) to ​(d).

A. There is a linear pattern to the​ data, so it is appropriate to carry out a linear regression.
B. There is a clear nonlinear pattern to the​ data, so it is inappropriate to carry out a linear regression.
C. There is no linear pattern to the​ data, so it is inappropriate to carry out a linear regression.
D. Not appropriate to carry out a linear regression.

(b) r squared=? ​(Round to four decimal places as​ needed.)
(c) Determine the percentage of variation in the observed values of the response variable explained by the​ regression, and interpret your answer. Select the correct choice below and fill in any answer boxes within your choice.
(d) State how useful the regression equation appears to be for making predictions.

A. Moderately useful
B. Not useful
C. Very useful
D. It is not reasonable to carry out a linear regression.

Answer 1

Answer:

Step-by-step explanation:

Given that a study on the relationship between the estriol levels of pregnant women and the birth weights of their children is given in the table.​ Here, x denotes estriol​ level, in​ mg/24 hr, and y denotes birth​ weight, in hectograms.

x y

15 33

25 39

21 34

18 33

27 44

12 25

19 35

16 32

 

r 0.943228963

r^2 0.889680876

Since r is near to 1, there is a good relation linear between x and y.

a) A. There is a linear pattern to the​ data, so it is appropriate to carry out a linear regression.

b) R^2 = 0.8897

c) The percentage of variation in the observed values of the response variable explained by the​ regression= 88.97

i.e. R^2represents the percentage of variation between the two variables.

d) C. Very useful, since here linear relation is strong.