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

What do the two regression parameters (b0 and b1) mean?

Answer 1

This exercise is solved using excel - Data Analysis - Regression function.
The needed equation and explaination about the coefficient in provide in line with output.

Put the data in excel as shown below.

In this case, musclemass(Y) is the dependent variable and age(x1) ,excercisetime(x2) are the independent variable.

Regression equation for Musclemass vs. age

Input the data in the Data analysis - regression table as shown below
and click ok.

The output will be provided as shown below.

Using the coefficients from the regression output we construct regression equation

y = 153.6755 - 1.15589 Age

In this case, the intercept (b0), indicate that the baseline muscle mass of a new born is 153.67 when age = 0
Interpretation of b1 : One unit increase in the age, decreases the muscle mass by 1.15589 units.
Here the p value for age is significant as it less than 0.05 and this variable is signicant in explaining the dependent variable.

Using the above equation now predict the muscle mass given the age of the person as shown below.

Regression equation for Musclemass vs. excerisetime.

We use the same procedure as explained above, the screenshot of the input in the regression tab and the output is given below.

y = 89.52787- 0.12608 Excerisetime

In this case, the intercept (b0), indicate with any excerise the musle mass would be about 89527
Interpretation of b1 : One unit increase in the excerisetime, decreases the muscle mass by 0.12608 units.
Here the p value for excercise is not significant as it more than 0.05 and this variable is not signicant in explaining the dependent variable.
Also intitutively, by doing excerise the muscle mass must increase hence the sign of the b1 is not correct

Since here the variable is not significant we not use this equation to predict musclemass