A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds). Two variables thought to affect
weight
loss are client's length of time on the weight-loss program and time of session. These variables are described below:
Y = Weight loss (in pounds)
X1 = Length of time in weight-loss program (in months) X2 = 1 if morning session, 0 if not
Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the model with interaction term:
Y=po+p1X1 + B2X2 + B3X1X2 + E
Output from Microsoft Excel follows:
Standard Error
P-value
Lower 99%
t Stat
Coefficients
Upper 99%
42.6106
22.3710
-84.0702
-20.7298
-0.9266
0.3646
Intercept
0.0001
3.0024
4.8340
11.4919
1.4992
7.2472
Length
2.2419
204.1138
0.0359
40.2336
-23.7176
Morn
90.1981
0.1428
-5.1024
3.3511
4.3857
-1.5226
-14.5905
Length X Morn
There is insufficient evidence (at a = 0.05) of curvature in the relationship between weight loss (Y) and months on program(X1).
There is sufficient evidence (at a = 0.05) of curvature in the relationship between weight loss (Y) and months on program (X1).
There is insufficient evidence (at a = 0.05) to indicate that the relationship between weight loss (Y) and months on program(X1) varies with session time.
There is sufficient evidence (at a = 0.05) to indicate that the relationship between weight loss (Y) and months on program (X1) varies with session time.

Question

Accepted Answer

⚹ Based on the information provided by the OCR model, we can analyze the regression output to determine the statistical significance of the coefficients and the interaction term. ⚹ ⚹ The p-value column in the regression output indicates whether the coefficients are statistically significant at the given alpha level (α = 0.05). A p-value less than 0.05 suggests that the coefficient is statistically significant. ⚹ ⚹ For the coefficient of 'Length', the p-value is 0.0001, which is less than 0.05, indicating that there is sufficient evidence to conclude that the length of time on the weight-loss program has a significant effect on weight loss. ⚹ ⚹ The coefficient of 'Morn' has a p-value of 0.0359, which is also less than 0.05, suggesting that the time of the session (morning or not) has a significant effect on weight loss. ⚹ ⚹ The interaction term 'Length X Morn' has a p-value of 0.1428, which is greater than 0.05, indicating that there is insufficient evidence to conclude that the relationship between weight loss and months on the program varies with session time. ⚹ ⚹ Therefore, we can conclude that there is sufficient evidence at α = 0.05 to indicate that both the length of time on the weight-loss program and the time of session (morning or not) have significant effects on weight loss, but there is insufficient evidence to support the presence of an interaction effect between these two variables. ⚹

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