Question

1. For 12 recent clients, a weight-loss clinic has collected the data shown in cells B3 to E14 on the answers sheet. For Session, day is coded as 1 and evening is coded as 0. For Gender, male is coded as 1 and female is coded as 0.
	a. Use Excel to carry out a multiple regression analysis of all of that data.
	b. Interpret each of the three partial regression coefficients.
	c. Conduct hypothesis tests at the 5% significance levels to determine whether each coefficient is significantly different from zero.

Pounds lost	Months as a client	Session (Day = 1)	Gender (Male =1)
31	5	1	1
49	8	1	1
12	3	1	0
26	9	0	0
34	8	0	1
11	2	0	0
4	1	0	1
27	8	0	1
12	6	1	1
28	9	1	0
41	6	0	0
16	6	0	0

Answer 1

a) Carrying out regression in Excel (go to Data tab -> Data Analysis -> Regression, choose Pounds Lost as Y-column, and Month, Session, Gender as X-columns), we get the following output:

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.243491016	8.875972951	0.25276001	0.80682711	-18.22453931	22.71152134
Months as a client	3.35606894	1.271435035	2.639591366	0.02973218	0.424134492	6.288003388
Session (Day = 1)	1.538320499	6.791107153	0.226519839	0.82647782	-14.12200068	17.19864168
Gender (Male =1)	3.01760176	6.671026106	0.452344469	0.6630347	-12.36581203	18.40101555

b) The partial regression coefficients for Months as a client is 3.356 => Pounds lost increases by about 3.356 per additional month as a client. It's low p-value (0.029) suggests it is a significant linear predictor of Pounds lost.

The partial regression coefficients for Session is 1.538 => Pounds lost is higher by about 1.538 if someone takes up day session rather than evening. However, the high p-value suggests the linear relationship of Session with Pounds lost is not significant.

The partial regression coefficients for Gender is 3.0176 => Pounds lost is higher by about 3.0176 if Gender is 1 or male, compared to female gender. However, the high p-value suggests the linear relationship of Gender with Pounds lost is not significant.

c) As discussed above, only Months as a client has p-value < 0.05, hence only Months as a client has a coefficient significantly different from 0 at 5% significance level. The other 2 variables, Session and Gender have p-value > 0.05, hence their coefficients aren't significantly different from 0 at a significance level of 5%.