Degree of freedom is defined as the minimum number of independent variables required to completely describe the state of physical system. Factors on whichdegree of freedom depends upon : 1. Atomicity of gas -- number of atoms present in a molecule of gas.

Introduction:
The concept of degrees of freedom is commonly used in statistics and refers to the number of independent pieces of information available to estimate a parameter or make an inference. The degrees of freedom are influenced by two main factors: sample size and the number of parameters being estimated. Understanding these factors is crucial in various statistical analyses.

1. Sample Size:
The sample size refers to the number of observations or data points available in a dataset. It is a crucial factor in determining the degrees of freedom. The larger the sample size, the greater the number of independent observations, resulting in more degrees of freedom. This is because a larger sample provides more information, reducing uncertainty and increasing the precision of estimates.

Impact on Degrees of Freedom:
- Large Sample Size: A larger sample size increases the degrees of freedom, allowing for more precise estimations. It reduces the risk of overfitting and provides a better representation of the population.
- Small Sample Size: Conversely, a smaller sample size decreases the degrees of freedom, limiting the accuracy and generalizability of estimations. It increases the risk of sampling error and may lead to less reliable results.

2. Number of Parameters:
The number of parameters being estimated in a statistical model is another crucial factor influencing degrees of freedom. Parameters are the unknown quantities in a model that need to be estimated using the available data. Each parameter estimation consumes degrees of freedom, as they represent independent pieces of information required for estimation.

Impact on Degrees of Freedom:
- Fewer Parameters: When the number of parameters to be estimated is small, more degrees of freedom are available for each parameter. This allows for more precise estimation of individual parameters as there are more independent pieces of information available for each.
- More Parameters: Conversely, when the number of parameters to be estimated is large, the degrees of freedom available for each parameter decrease. This can lead to less precise estimations and increase the risk of overfitting the data.

Conclusion:
In summary, the degrees of freedom in statistical analyses depend on two main factors: the sample size and the number of parameters being estimated. A larger sample size provides more independent observations, increasing the degrees of freedom and allowing for more precise estimations. Conversely, a smaller sample size reduces degrees of freedom, limiting the accuracy of estimations. The number of parameters being estimated also impacts degrees of freedom, with fewer parameters allowing for more precise estimations and vice versa. Understanding these factors is essential for conducting reliable statistical analyses and making accurate inferences.