A study was conducted to investigate whether gestational age

A study was conducted to investigate whether gestational age at birth (in weeks) predicts birth weight (in grams). The following data were collected:

Infant ID

Age at birth (weeks)

Birth weight (g)

1

34.7

1895

2

36.0

2030

3

29.3

1440

4

40.1

2835

5

35.7

3090

6

42.4

3827

7

40.3

3260

8

37.3

2690

9

40.9

3285

10

38.3

2920

11

38.5

3430

12

41.4

3657

13

39.7

3685

14

39.7

3345

15

41.1

3260

16

38.0

2680

17

38.7

2005

Please show your work in answering the following (you may use R):

a) Find the slope of the regression line and interpret the slope.

b) Find the Y-intercept of the regression line.

c) Write down the regression equation.

d) Create a scatterplot showing age vs birth weight and indicate what kind of relationship you see between the two variables. Add the regression line to the plot.

e) Find the predicted birth weight (Y’) for each observed age.

f) Find the residuals for each subject and the SS_Residual.

g) Find the standard error of estimate (s_Y.X) using SS_Residual.

h) Find r_obs for age and weight.

i) Find the standard error of estimate (s_Y.X) using r_obs.

j) Compare s_Y.X in g and i and briefly explain what s_Y.X tells us with respect to the linear relation between age and weight.

k) Write the overall conclusion from this analysis

Infant ID	Age at birth (weeks)	Birth weight (g)
1	34.7	1895
2	36.0	2030
3	29.3	1440
4	40.1	2835
5	35.7	3090
6	42.4	3827
7	40.3	3260
8	37.3	2690
9	40.9	3285
10	38.3	2920
11	38.5	3430
12	41.4	3657
13	39.7	3685
14	39.7	3345
15	41.1	3260
16	38.0	2680
17	38.7	2005

Solution