Concept explainers
For a linear equation y = b0 + b1x1 + b2x2 + b3x3, identify the
- a. independent variables.
- b. dependent variable.
- c. y-intercept.
- d. partial slopes.
a.
Identify the independent variables in the linear equation
Answer to Problem 1RP
The independent variables in the linear equation
Explanation of Solution
Justification:
Independent variable:
An independent variable in the multiple regression analysis is the variable which explains the variation in the response variable and which itself does not depend on any other variables in the regression. The predictor variables are the independent variables.
In the linear equation
Thus, the independent variables in the linear equation
b.
Identify the dependent variable in the linear equation
Answer to Problem 1RP
The dependent variable in the linear equation
Explanation of Solution
Justification:
Dependent variable:
A dependent variable in the multiple regression analysis is the variable the variation in which is explained by the predictor variables. The response variable is the dependent variable.
In the linear equation
Thus, the independent variables in the linear equation
c.
Identify the y-intercept in the linear equation
Answer to Problem 1RP
The y-intercept in the linear equation
Explanation of Solution
Justification:
The y-intercept:
The y-intercept in a multiple linear regression equation is the value taken by the response variable y, when all the predictor variables take value 0. The y-intercept gives the value of y at the point where the plane intersects the y-axis.
In a linear equation of the form,
Thus, the y-intercept in the linear equation
d.
Identify the partial slopes in the linear equation
Answer to Problem 1RP
The partial slopes in the linear equation
Explanation of Solution
Justification:
Partial slope:
The partial slope corresponding to a predictor variable in a multiple linear regression equation is a measure of the steepness of the plane along the direction of that predictor variable. The partial slope is the change in the response variable y, when the particular predictor variable increases by one unit, keeping all other predictor variables fixed.
In a linear equation of the form,
Thus, the partial slopes in the linear equation
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