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Instruction 13 $Y =$ Weight-Loss (In Kilograms) $X _ { 1 } =$

question 171

Multiple Choice

Instruction 13.38
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms) . Two variables thought to effect 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 kilograms)
$X _ { 1 } =$ Length of time in weight-loss program (in months)
$x _ { 2 } = 1$ if morning session, 0 if not
$x _ { 3 } = 1$ 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:
$Y = \beta 0 + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 3 } + \beta _ { 4 } X _ { 1 } X _ { 2 } + \beta _ { 5 } X _ { 1 } X _ { 3 } + \varepsilon$
Partial output from Microsoft Excel follows:
$Instruction 13.38 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms) . Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session. These variables are described below: Y = Weight-loss (in kilograms) X _ { 1 } = Length of time in weight-loss program (in months) x _ { 2 } = 1 if morning session, 0 if not x _ { 3 } = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = \beta 0 + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 3 } + \beta _ { 4 } X _ { 1 } X _ { 2 } + \beta _ { 5 } X _ { 1 } X _ { 3 } + \varepsilon Partial output from Microsoft Excel follows: -Referring to Instruction 13.38,in terms of the ?s in the model,give the mean change in weight-loss (Y) for every 1 month increase in time in the program (X1) when attending the morning session. A) \beta 1 + \beta 4 B) \beta 1 + \beta 5 C) \beta 1 D) \beta 4 + \beta 5$
-Referring to Instruction 13.38,in terms of the ?s in the model,give the mean change in weight-loss (Y) for every 1 month increase in time in the program (X₁) when attending the morning session.

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Definitions:

Regression Analysis

A statistical method for estimating the relationships among variables, including a dependent variable and one or more independent variables.

Least Squares Line

A straight line that minimizes the sum of the squared differences between observed values and the values predicted by the line.

Increase In Sales

A measure indicating the growth in revenue generated from goods sold or services provided over a specific period.

Least Squares Line

A line of best fit determined by minimizing the sum of the squares of the vertical deviations from each data point to the line.

Instruction 13 Y=Y =Y= Weight-Loss (In Kilograms) X1=X _ { 1 } =X1​=

Definitions:

Instruction 13 $Y =$ Weight-Loss (In Kilograms) $X _ { 1 } =$