Residual Standard Error of Data given Degrees of Freedom Solution

STEP 0: Pre-Calculation Summary
Formula Used
Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error)
RSEData = sqrt(RSS(Error)/DF(Error))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Residual Standard Error of Data - Residual Standard Error of Data is the measure of the spread of residuals (differences between observed and predicted values) around the regression line in a regression analysis.
Residual Sum of Squares in Standard Error - Residual Sum of Squares in Standard Error is the sum of the squared differences between observed and predicted values in a regression analysis.
Degrees of Freedom in Standard Error - Degrees of Freedom in Standard Error is the number of values in the final calculation of a statistic that are free to vary.
STEP 1: Convert Input(s) to Base Unit
Residual Sum of Squares in Standard Error: 400 --> No Conversion Required
Degrees of Freedom in Standard Error: 99 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RSEData = sqrt(RSS(Error)/DF(Error)) --> sqrt(400/99)
Evaluating ... ...
RSEData = 2.01007563051842
STEP 3: Convert Result to Output's Unit
2.01007563051842 --> No Conversion Required
FINAL ANSWER
2.01007563051842 2.010076 <-- Residual Standard Error of Data
(Calculation completed in 00.004 seconds)

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Errors Calculators

Standard Error of Proportion
​ LaTeX ​ Go Standard Error of Proportion = sqrt((Sample Proportion*(1-Sample Proportion))/Sample Size in Standard Error)
Residual Standard Error of Data given Degrees of Freedom
​ LaTeX ​ Go Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error)
Standard Error of Data given Variance
​ LaTeX ​ Go Standard Error of Data = sqrt(Variance of Data in Standard Error/Sample Size in Standard Error)
Standard Error of Data
​ LaTeX ​ Go Standard Error of Data = Standard Deviation of Data/sqrt(Sample Size in Standard Error)

Residual Standard Error of Data given Degrees of Freedom Formula

​LaTeX ​Go
Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error)
RSEData = sqrt(RSS(Error)/DF(Error))

What is Standard Error and it's importance?

In Statistics and data analysis standard error has great importance. The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.
The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

How to Calculate Residual Standard Error of Data given Degrees of Freedom?

Residual Standard Error of Data given Degrees of Freedom calculator uses Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error) to calculate the Residual Standard Error of Data, Residual Standard Error of Data given Degrees of Freedom formula is defined as the measure of the spread of residuals (differences between observed and predicted values) around the regression line in a regression analysis, and calculated using the degrees of freedom of the data. Residual Standard Error of Data is denoted by RSEData symbol.

How to calculate Residual Standard Error of Data given Degrees of Freedom using this online calculator? To use this online calculator for Residual Standard Error of Data given Degrees of Freedom, enter Residual Sum of Squares in Standard Error (RSS(Error)) & Degrees of Freedom in Standard Error (DF(Error)) and hit the calculate button. Here is how the Residual Standard Error of Data given Degrees of Freedom calculation can be explained with given input values -> 0.752101 = sqrt(400/99).

FAQ

What is Residual Standard Error of Data given Degrees of Freedom?
Residual Standard Error of Data given Degrees of Freedom formula is defined as the measure of the spread of residuals (differences between observed and predicted values) around the regression line in a regression analysis, and calculated using the degrees of freedom of the data and is represented as RSEData = sqrt(RSS(Error)/DF(Error)) or Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error). Residual Sum of Squares in Standard Error is the sum of the squared differences between observed and predicted values in a regression analysis & Degrees of Freedom in Standard Error is the number of values in the final calculation of a statistic that are free to vary.
How to calculate Residual Standard Error of Data given Degrees of Freedom?
Residual Standard Error of Data given Degrees of Freedom formula is defined as the measure of the spread of residuals (differences between observed and predicted values) around the regression line in a regression analysis, and calculated using the degrees of freedom of the data is calculated using Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error). To calculate Residual Standard Error of Data given Degrees of Freedom, you need Residual Sum of Squares in Standard Error (RSS(Error)) & Degrees of Freedom in Standard Error (DF(Error)). With our tool, you need to enter the respective value for Residual Sum of Squares in Standard Error & Degrees of Freedom in Standard Error and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Residual Standard Error of Data?
In this formula, Residual Standard Error of Data uses Residual Sum of Squares in Standard Error & Degrees of Freedom in Standard Error. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/(Sample Size in Standard Error-1))
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