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# Degrees of Freedom

The number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move without violating any constraint imposed on it, is called degree of freedom. The degree of freedom can be defined as the minimum number of independent coordinates which can specify the position of the system completely. Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom.

Mathematically, the degrees of freedom are the number of dimensions of the domain of a random vector, or essentially the number of free components: how many components need to be known before the vector is fully determined. The term is often used in the context of linear models. The degrees of freedom are also associated with the squared lengths of such vectors and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.

The common way to think of degrees of freedom is as the number of independent pieces of information available to estimate another piece of information. The number of degrees of freedom is the number of independent observations in a sample of data that are available to estimate a parameter of the population from which that sample is drawn.

### F-Ratio with Degrees of Freedom of 1 and 18.

A researcher who is evaluating the significance of a regression equation with one predictor variable obtains an F-ratio with df of 1 and 18. How many pairs of scores, x and y values, are in the data?

### Fill in the missing values

The following table summarizes the results from a 2 factor study with levels of factor A and 3 levels of factor B using a separate sample of n-=8 participants in each treatment condition. Fill in the missing values,start with df. Source ss df MS Bet/ treatments 60 Factor A

### Degrees of Freedom for Related Populations

If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to 39 19 18 Show all work.

### Calculate the chi-square statistic and degrees of freedom

Calculate the chi-square statistic and degrees of freedom for the following set of data for 300 people: Group A Group B Group C Total Had flu shot 20 45 25 90 Didn't have flu shot 80 55 75 210 Total 100 100 100 300 Is the value of the chi-square statis

### Probability and Degrees of Freedom Analysis with Excel

PROBLEM: Compute the following probabilities using excel: (a) P (t10 &#8805; 1.75) where t10 has a t distribution with 10 degrees of freedom. (b) P (t100 &#8805; 1.75) where t100 has a t distribution with 100 degrees of freedom. How do you explain the difference between this result and the one obtained in part (a)?

### Degrees of Freedom

A machine is set to fill the small size packages of M&M candies with 56 candies per bag. A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many degrees of freedom are there? a. 9 b. 1 c. 8 d. 7

### 3702- stats

1. The following data CELLPHONE represent the digital-mode talk time in hours and the battery capacity in milliampere-hours of cell phones. Name Type Price Talk Time Battery Capacity Samsung SPH-N200 CDMA 200 4.5 800 Nokia 6185 CDMA 99 4 1500 Sanyo SCP-4500 CDMA 180 3 1300 Kyocera Smart Phone QCP-6035 CDMA 450 2 1550