R

(noun)

A free software programming language and a software environment for statistical computing and graphics.

Related Terms

  • TI-83

Examples of R in the following topics:

  • Values of the Pearson Correlation

    • Pearson's r can range from -1 to 1.
    • An r of -1 indicates a perfect negative linear relationship between variables, an r of 0 indicates no linear relationship between variables, and an r of 1 indicates a perfect positive linear relationship between variables.
    • Figure 1 shows a scatter plot for which r = 1.
    • A scatter plot for which r = 0.
    • Scatter plot of Grip Strength and Arm Strength, r = 0.63
  • The Correlation Coefficient r

    • The value of r is always between -1 and +1: − 1 ≤ r ≤ 1.
    • If r = 1, there is perfect positive correlation.
    • If r = − 1, there is perfect negative correlation.
    • The formula for r looks formidable.
    • (a) A scatter plot showing data with a positive correlation. 0 < r < 1 (b) A scatter plot showing data with a negative correlation. − 1 < r < 0 (c) A scatter plot showing data with zero correlation. r=0
  • Randomization Tests: Association (Pearson's r)

    • A significance test for Pearson's r is described in the section inferential statistics for b and r.
    • This section describes a method for testing the significance of r that makes no distributional assumptions.
    • This arrangement is shown in Table 2 and the r is 0.945.
    • Note that this is a one-tailed probability since it is the proportion of arrangements that give an r as large or larger.
    • The example data arranged to give the highest r
  • Sampling Distribution of Pearson's r

    • State how the shape of the sampling distribution of r deviates from normality
    • Calculate the probability of obtaining an r above a specified value
    • The distribution of values of r after repeated samples of 12 students is the sampling distribution of r.
    • The sampling distribution of r for N = 12 and ρ = 0.60.
    • The sampling distribution of r for N = 12 and ρ = 0.90.
  • References

    • R., Bradley, T.
    • D. (1979) Type I error rate of the chi square test of independence in r x c tables that have small expected frequencies.
  • Using a Statistical Calculator

    • Two of the most common calculators in use are the TI-83 series and the R statistical software environment.
    • Polls and surveys of data miners are showing R's popularity has increased substantially in recent years.
    • R was created by Ross Ihaka and Robert Gentleman at the University of Auckland, New Zealand, and is currently developed by the R Development Core Team, of which Chambers is a member.
    • R is easily extensible through functions and extensions, and the R community is noted for its active contributions in terms of packages.
    • Analyze the use of R statistical software and TI-83 graphing calculators
  • Testing the Significance of the Correlation Coefficient

    • If r < negative critical value or r > positive critical value, then r is significant.
    • Since r = 0.801 and 0.801 > 0.632, r is significant and the line may be used for prediction.
    • r = 0.708 and the sample size, n, is 9.
    • r = 0 and the sample size, n, is 5.
    • No matter what the dfs are, r = 0 is between the two critical values so r is not significant.
  • Notation for the Hypergeometric: H = Hypergeometric Probability Distribution Function X ~ H (r,b,n)

    • Read this as "X is a random variable with a hypergeometric distribution. " The parameters are r, b, and n. r = the size of the group of interest (first group), b = the size of the second group, n = the size of the chosen sample
    • X takes on the values 0, 1, 2, 3, 4, where r = 6, b = 5 , and n = 4.
    • The formula for the mean is µ = (n.r)/(r + b) = (4 .6)/(6 + 5) = 2.18
  • Coefficient of Determination

    • In context of data, $r^2$ can be interpreted as follows:
    • An $r^2$ of 1 indicates that the regression line perfectly fits the data.
    • This illustrates a drawback to one possible use of $r^2$, where one might keep adding variables to increase the $r^2$ value.
    • This leads to the alternative approach of looking at the adjusted $r^2$.
    • The correlation coefficient is $r=0.6631$.
  • Summary

    • The closer r is to 1 or -1, the closer the original points are to a straight line.
    • If r is negative, the slope is negative.
    • If r is positive, the slope is positive.
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