The graph of the prediction equation obtained from fitting the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$
Is a(n):
A)Line
B)Plane
C)Parabola
D)Exponential curve
E)Single point

Question

Quizplus · Accepted Answer

The equation $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$ represents a linear model with two predictors, $X_1$ and $X_2$. The graph of this equation in a three-dimensional space (with axes for $X_1$, $X_2$, and $y$) is a plane. Each term is linear, and there are no squared terms or other nonlinear transformations, so the graph is not a parabola or an exponential curve. It's not a line because there are two independent variables, and it's not a single point because the equation represents a relationship across a range of $X_1$ and $X_2$ values.

The Graph of the Prediction Equation Obtained from Fitting the Model