Question

Using MS Excel and the random number generator function, generate values for 30 observations for the following columns with average daily:

1. Body weight with random values between 100 and 250lbs

2. Calories intake with random values between 1000 and 3000

   calories

3. Workout duration with random values between 0 and 60 minutes

4. Sleep duration with random values between 2 and 12 hours

5. Work duration with random values between 0 and 12 hours

1. Assuming that the values are averages over 1 year, conduct the following:

   1. Descriptive statistics for each category
   2. Correlation analysis between weight and calorie intake 3. Analysis of variance
   4. Regression analysis

2. Formulate a hypothesis of your choice using weight, calorie intake, workout duration, sleep duration, and/or work duration. Which statistical test would you select to validate the hypothesis?

3. What are your observations?

Answer 1

Let

y denotes, Body weight ; x1 denotes Calories Intake ; x2 denotes Work Duration ; x3 denotes Sleep Duration ; x4 denotes Work Duration

Random values generated as per the given conditions are

S.No.	y	x1	x2	x3	x4
1	180	1938	7	2	5
2	149	1783	58	9	11
3	166	2974	37	11	0
4	183	1540	58	11	7
5	173	2247	14	2	6
6	135	2398	21	3	3
7	124	2274	57	10	9
8	172	2545	43	3	2
9	108	2194	59	2	9
10	193	2678	25	4	8
11	191	1867	14	4	10
12	237	1412	4	4	7
13	190	1711	4	12	8
14	192	1018	30	7	8
15	184	1090	60	5	3
16	234	2080	31	8	8
17	192	1758	40	10	12
18	232	2107	48	4	4
19	179	1701	8	10	4
20	212	2818	44	9	3
21	207	2758	10	8	7
22	213	2105	28	3	1
23	179	2278	37	5	6
24	184	2359	58	7	4
25	171	2901	21	8	0
26	113	1734	22	5	1
27	211	2242	51	10	6
28	163	1253	55	7	0
29	246	2069	9	5	0
30	199	1014	48	12	4

1. Descriptive Statistics for each category are

2. Correlation between Body Weight and Calories Intake is

Let us regress Body Weight (y) on Calories Intake (x1), Workout Duration (x2), Sleep Duration (x3), and Work Duration (x4) i.e.,

The linear regression equation is

... (1)

Where

Our hypothesis is to test is at least one of the regressors are statistically significantly i.e.,

Null hypothesis

versus

Alternative hypothesis

for at least one j = 1,2,3,4

(3)

Analysis of variance table is given below

From p-value (Significance F) = 0.5486 > 0.05, it is inferred that we do not reject Null hypothesis and infer that none of the independent variables considered in the equation (1) are statistically significant in explaining the dependent variable

(4)

Regression Analysis table is given below:

From the 'Summary Output' it is inferred that

a. Considering p-values of individual parameters, all p-values > 0.05 leading us to conclude that the parameter estimates are not statistically significant from '0'.

b. Considering R-Square (=0.1109), inferring that the regressor variables could only explain 11.09% of the total variation in the dependent variable, which indicates that these regressor variables are not sufficient to explain the dependent variable