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) X 1 Length of time in weight loss program (in months) X 2 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 interaction model Y 0 1 X 1 2 X 2 3 X 1 X 2 Output from Microsoft Excel follows Regression Statistics Multiple R 0 7308 R Square 0 5341 Adjusted R Square 0 4675 Standard Error 43 3275 Observations 25 ANOVA df SS MS F Significance F Regression 3 45194 0661 15064 6887 8 0248 0 0009 Residual 21 39422 6542 1877 2692 Total 24 84616 7203 Coefficients Standard Error t Stat P value Lower 99 Upper 99 Intercept 20 7298 22 3710 0 9266 0 3646 84 0702 42 6106 Length 7 2472 1 4992 4 8340 0 0001 3 0024 11 4919 Mom 90 1981 40 2336 2 2419 0 0359 23 7176 204 1138 Length x Morn 5 1024 3 3511 1 5226 0 1428 14 5905 4 3857

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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

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)

X ₁= Length of time in weight-loss program (in months)

X ₂= 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 interaction model:

Y=? ₀+? ₁X ₁+? ₂X ₂+? ₃X ₁X ₂+?

Output from Microsoft Excel follows:

Regression Statistics Multiple R 0.7308 R Square 0.5341 Adjusted R Square 0.4675 Standard Error 43.3275 Observations 25 ANOVA df SS MS F Significance F Regression 3 45194.0661 15064.6887 8.0248 0.0009 Residual 21 39422.6542 1877.2692 Total 24 84616.7203 Coefficients Standard Error t Stat P-value Lower 99% Upper 99% Intercept -20.7298 22.3710 -0.9266 0.3646 -84.0702 42.6106 Length 7.2472 1.4992 4.8340 0.0001 3.0024 11.4919 Mom 90.1981 40.2336 2.2419 0.0359 -23.7176 204.1138 Length x Morn -5.1024 3.3511 -1.5226 0.1428 -14.5905 4.3857