Respuesta :
Answer:
b) y = 289.815 when [tex]x_1 = 180 \text{ and } x_2 = 310[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]y = 29.1270 + 0.5906x_1 + 0.4980x_2[/tex]
where y is the dependent variable,
[tex]x_1, x_2[/tex] are the independent variable.
The multiple regression equation is of the form:
[tex]y = b_0 + b_1x_1 + b_2x_2[/tex]
where,
[tex]b_0[/tex]: is the intercept of the equation and is the value of dependent variable when all the independent variable are zero.
[tex]b_1[/tex]: It is the slope coefficient of the independent variable [tex]x_1[/tex].
[tex]b_2[/tex]: It is the slope coefficient of the independent variable [tex]x_2[/tex].
- The regression coefficient in multiple regression is the slope of the linear relationship between the dependent and the part of a predictor variable that is independent of all other predictor variables.
Comparing the equations, we get:
[tex]b_1 = 0.5906\\b_2 = 0.4980[/tex]
- This means holding [tex]x_2[/tex] constant, a change of one in [tex]x_1[/tex] is associated with a change of 0.5906 in the dependent variable.
- This means holding [tex]x_1[/tex] constant, a change of 1 in [tex]x_2[/tex] is associated with a change of 0.4980 in the dependent variable.
b) We have to estimate the value of y
[tex]y = 29.1270 + 0.5906(180) + 0.4980(310) = 289.815[/tex]
