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TABLE 17-6 A Weight-Loss Clinic Wants to Use Regression Analysis to Build

Question 114

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TABLE 17-6
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
X3 = 1 if afternoon session,0 if not (Base level = evening session)
Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model:
Y = β0 + β1X1 + β2X2 + β3X3 + β4X1X2 + β5X1X3 + ε
Partial output from Microsoft Excel follows:
Regression Statistics TABLE 17-6 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<sub>1 </sub>= Length of time in weight-loss program (in months) X<sub>2</sub> = 1 if morning session,0 if not X<sub>3</sub> = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β<sub>0</sub> + β<sub>1</sub>X<sub>1</sub> + β<sub>2</sub>X<sub>2</sub> + β<sub>3</sub>X<sub>3</sub> + β<sub>4</sub>X<sub>1</sub>X<sub>2</sub> + β<sub>5</sub>X<sub>1</sub>X<sub>3</sub> + ε Partial output from Microsoft Excel follows: Regression Statistics ANOVA F = 5.41118 Significance F = 0.040201 -Referring to Table 17-6,what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time in the program (X<sub>1</sub>) varies according to time of session? A) H<sub>0 </sub> : β<sub>1 </sub>= β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = β<sub>5 </sub>= 0 B) H<sub>0</sub> : β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = β<sub>5 </sub>= 0 C) H<sub>0</sub> : β<sub>4</sub> = β<sub>5 </sub>= 0 D) H<sub>0</sub> : β<sub>2</sub> = β<sub>3</sub> = 0 ANOVA
F = 5.41118 Significance F = 0.040201 TABLE 17-6 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<sub>1 </sub>= Length of time in weight-loss program (in months) X<sub>2</sub> = 1 if morning session,0 if not X<sub>3</sub> = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β<sub>0</sub> + β<sub>1</sub>X<sub>1</sub> + β<sub>2</sub>X<sub>2</sub> + β<sub>3</sub>X<sub>3</sub> + β<sub>4</sub>X<sub>1</sub>X<sub>2</sub> + β<sub>5</sub>X<sub>1</sub>X<sub>3</sub> + ε Partial output from Microsoft Excel follows: Regression Statistics ANOVA F = 5.41118 Significance F = 0.040201 -Referring to Table 17-6,what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time in the program (X<sub>1</sub>) varies according to time of session? A) H<sub>0 </sub> : β<sub>1 </sub>= β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = β<sub>5 </sub>= 0 B) H<sub>0</sub> : β<sub>2</sub> = β<sub>3</sub> = β<sub>4</sub> = β<sub>5 </sub>= 0 C) H<sub>0</sub> : β<sub>4</sub> = β<sub>5 </sub>= 0 D) H<sub>0</sub> : β<sub>2</sub> = β<sub>3</sub> = 0
-Referring to Table 17-6,what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time in the program (X1) varies according to time of session?


A) H0 : β1 = β2 = β3 = β4 = β5 = 0
B) H0 : β2 = β3 = β4 = β5 = 0
C) H0 : β4 = β5 = 0
D) H0 : β2 = β3 = 0

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