In: Statistics and Probability
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 |
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%.