Question

For simple linear regression, y = β0 + β1x + u, which one of the following statements is true?

a. u is called the "error term". It is the error we make in prediction and b. u is called disturbance and it can be observed. c. u includes everything that affects y other than x. d. x is called the independent variable because x is independent from y and u.

Answer 1

Option a) u is called the "error term". It is the error we make in prediction

Option d) x is called the independent variable because x is independent from y and u.

Explanation:

We are given the following information in the question:

`y = \beta_0 + \beta_1x + u`

where y is the dependent variable, x is the independent variable.

`\beta_0`: It is the value of y when x is zero, that is y-intercept.

`\beta_1`: It is the coefficient of x in predicting the dependent variable y.

u is the error term.

• An error term represents the margin of error.
• It refers to the sum of the deviations within the regression line, that is the difference between the predicted value and the observed value of y.

Thus, Option A) u is the error term and Option D) x is called the independent variable because x is independent from y and u are the correct answer.