Question

In: Statistics and Probability

1. For 12 recent clients, a weight-loss clinic has collected the data shown in cells B3...

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

Solutions

Expert Solution

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%.


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