Question

A person’s muscle mass is expected to be associated with age. Some people also thought exercise time would be associated with the muscle mass. To explore the potential relationships between muscle mass and age, muscle mass and exercise time, a nutritionist randomly selected 20 women from a population of women with age ranging from 40 to 80 years old, and measured their muscle mass (a score without unit) and exercise time (hours per month)

Patient	Age	MuscleMass	ExcerciseTime
1	43	106	23
2	41	106	24
3	47	97	26
4	76	56	21
5	72	70	23
6	76	74	19
7	42	105	22
8	49	97	17
9	53	92	14
10	44	103	21
11	63	80	25
12	55	90	16
13	66	77	25
14	58	86	19
15	70	72	18
16	57	87	22
17	71	71	21
18	46	100	18
19	61	83	27
20	68	74	20
21	44	105	21
22	53	94	19
23	60	82	23
24	72	78	21

Using the regression equation representing the SIGNIFICANT relationship, make the following predictions: [of note: based on the regression model you chose, information for one of Age and ExcercieTime is not needed for prediction, but you should make your own decision on which variable is not needed!]

The expected Muscle Mass (the mean) for Women at Age= 65 and ExerciseTime = 20; (4 points)

The expected difference in Muscle Mass between women with Age = 55 and ExcerciseTme =23 and women with Age = 58 and ExcerciseTime=25. (4 points)

Answer 1

As per company policies, I am answering question one only.

Q1)

Model 1:

MuscleMass = 153.67-1.1558*Age

Ho: the model is not significant. H1: the model is significant.

With (F=370.81, P<5%), I reject the null hypothesis at 5% level of significance. And conclude that model 1 is significant.

Model 2:

MuscleMass = 89.53 - 0.126*ExcerciseTime

Ho: the model is not significant. H1: the model is significant.

With (F=0.0187, P<5%), I fail to reject the null hypothesis at 5% level of significance. And conclude that model 2 is NOT significant.