Question

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _______ 

a. the variance 

b. a residual 

c. a prediction interval 

d. the standard error

Answer 1

Concepts and reason

The least squares regression line is the unique line such that the sum of the squared vertical (y) distance between the data points and the line is the smallest possible.

The least squares regression line of y on x is the line that makes the sum of the squared residuals as small as possible.

Fundamentals

The least regression line $y{\rm{ on }}x$ is, $\hat y = a + bx$

Here, $y$ represents the dependent variable

$x$ represents the independent variable

$a$ represents the intercept variable

$b$ represents the slope variable.

The residual formula is, ${\rm{Residual}} = {\rm{Observed}} - {\rm{Predicted}}$

The available statement is the difference between the observed value of the dependent and the value of the predicted by using the regression equation.

A residual is the vertical difference between each data point and the regression line.

The correct answer is: B

Residual

The difference between the observed value of the dependent and the value of the predicted by using the regression equation is residual

Ans:

The correct answer is Residual.

Answer 2

The difference between the observed value of the dependent vanable and the value predicted by using the estimated regression equation is called Ang: b. a residual option b correct Explanation: The difference between the observed value of dependent variable the predicted variable cy) is called a residual. It is denoted by Each data point has one residual cy) and e e = observed value predicted value e = yay Both the sum and the mean of the residuals are equal to Zero j.e and ē =0