Question

Select the statements that are true of the population regression line. The population regression lineA. is defined in terms of two population parameters representing the slope and intercept.
B. assumes that the mean response has a straight-line relationship with the explanatory variable x.C. predicts the mean response for each value of the explanatory variable x.D. features known parameters representing the slope and intercept.E. is based on sample data.

Answer 1

Answer:

Correct statements are: (A), (B) and (C).

Step-by-step explanation:

A population regression line is of the form:

$Y_{i}=\beta_{0}+\beta_{1}X_{i}+\epsilon_{i}$

Here:

Y = response variable

X = explanatory variable

β₀ = intercept

β₁ = slope

ε = error term

The population parameters are β₀ and β₁.

The mean value of the response variable has a straight line relationship with the explanatory variables.

$E(Y_{i})=\beta_{0}+\beta_{1}E(X_{i})$

The value of the response variable can be computed using the explanatory variable values.

The population regression line is computed using the population data values.

Thus, the statements correct about the population regression line are (A), (B) and (C).