Question

In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the _____. slope error term variance standard error of the mean standard deviation

Answer 1

In regression analysis, deviations of actual Y values from the regression line are known as residuals or errors. Positive residuals mean the line underestimates Y, while negative residuals mean an overestimation. The standard deviation of residuals estimates the population standard deviation of Y.

Step-by-step explanation:

In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the residuals or errors. They are not errors in the sense of a mistake, but rather the differences between the observed data values and the values predicted by the regression line. A positive residual indicates that the actual data value for Y is higher than the predicted value (the point lies above the regression line), while a negative residual indicates that the actual data value is lower (the point lies below the regression line).

The absolute value of a residual measures the vertical distance between the actual value of Y and the estimated value (predicted by the regression line). Standard deviation of the residuals is used to estimate the population standard deviation of Y, denoted as s, and is calculated as s = √(SSE/n-2), where SSE represents the sum of squared errors.

Answer 2

Error term

Step-by-step explanation:

Given :

In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the _____. slope error term variance standard error of the mean standard deviation

To find :

Fill in the blanks.

Now, In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the Error term.

Because we use the error term in the regression analysis difference between the actual value of
`Y` and the approximate value of
`Y` which is above of actual value or below of actual value.

As
`Y`is an actual value and
`Y_0` is an approximate value then,

`|Y-Y_0|` is an error.

It is a vertical distance between the actual value and the approximate value of
`Y`.

So, the error term is always positive.