Residual Sum of Squares given Residual Standard Error Solution

STEP 0: Pre-Calculation Summary
Formula Used
Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1)
RSS = (RSE^2)*(N(SS)-1)
This formula uses 3 Variables
Variables Used
Residual Sum of Squares - Residual Sum of Squares is the sum of the squared differences between observed and predicted values in a regression analysis.
Residual Standard Error - Residual Standard Error is the measure of the spread of residuals (the differences between observed and predicted values) around the regression line.
Sample Size in Sum of Square - Sample Size in Sum of Square is the number of observations or data points collected in a study or experiment.
STEP 1: Convert Input(s) to Base Unit
Residual Standard Error: 2 --> No Conversion Required
Sample Size in Sum of Square: 15 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RSS = (RSE^2)*(N(SS)-1) --> (2^2)*(15-1)
Evaluating ... ...
RSS = 56
STEP 3: Convert Result to Output's Unit
56 --> No Conversion Required
FINAL ANSWER
56 <-- Residual Sum of Squares
(Calculation completed in 00.014 seconds)

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National Institute of Technology (NIT), Jamshedpur
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3 Sum of Squares Calculators

Residual Sum of Squares
​ Go Residual Sum of Squares = (Residual Standard Error^2)*Degrees of Freedom in Sum of Squares
Residual Sum of Squares given Residual Standard Error
​ Go Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1)
Sum of Squares
​ Go Sum of Squares = Variance of Data*Sample Size in Sum of Square

Residual Sum of Squares given Residual Standard Error Formula

Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1)
RSS = (RSE^2)*(N(SS)-1)

What is the importance of Sum of Squares of data values in Statistics?

In Statistics, the calculation of sum of squares has a great importance in both basic level and advanced level. For the basic measures of dispersions like variance, standard deviation, standard error, etc the calculations will be very hectic if we follow the summation from definition of them. But those summation can be simplified to another form which involves the sum of squares of the data points. Then the calculations will be easier and by squaring each value we can avoid the issues of negative signs when some data values are negative.

How to Calculate Residual Sum of Squares given Residual Standard Error?

Residual Sum of Squares given Residual Standard Error calculator uses Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1) to calculate the Residual Sum of Squares, Residual Sum of Squares given Residual Standard Error formula is defined as the sum of the squared differences between observed and predicted values in a regression analysis, and calculated using the residual standard error of the data. Residual Sum of Squares is denoted by RSS symbol.

How to calculate Residual Sum of Squares given Residual Standard Error using this online calculator? To use this online calculator for Residual Sum of Squares given Residual Standard Error, enter Residual Standard Error (RSE) & Sample Size in Sum of Square (N(SS)) and hit the calculate button. Here is how the Residual Sum of Squares given Residual Standard Error calculation can be explained with given input values -> 56 = (2^2)*(15-1).

FAQ

What is Residual Sum of Squares given Residual Standard Error?
Residual Sum of Squares given Residual Standard Error formula is defined as the sum of the squared differences between observed and predicted values in a regression analysis, and calculated using the residual standard error of the data and is represented as RSS = (RSE^2)*(N(SS)-1) or Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1). Residual Standard Error is the measure of the spread of residuals (the differences between observed and predicted values) around the regression line & Sample Size in Sum of Square is the number of observations or data points collected in a study or experiment.
How to calculate Residual Sum of Squares given Residual Standard Error?
Residual Sum of Squares given Residual Standard Error formula is defined as the sum of the squared differences between observed and predicted values in a regression analysis, and calculated using the residual standard error of the data is calculated using Residual Sum of Squares = (Residual Standard Error^2)*(Sample Size in Sum of Square-1). To calculate Residual Sum of Squares given Residual Standard Error, you need Residual Standard Error (RSE) & Sample Size in Sum of Square (N(SS)). With our tool, you need to enter the respective value for Residual Standard Error & Sample Size in Sum of Square 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 Sum of Squares?
In this formula, Residual Sum of Squares uses Residual Standard Error & Sample Size in Sum of Square. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Residual Sum of Squares = (Residual Standard Error^2)*Degrees of Freedom in Sum of Squares
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