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- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./07%3A_Introduction_to_Linear_Regression/7.02%3A_Line_Fitting_Residuals_and_CorrelationIn this section, we examine criteria for identifying a linear model and introduce a new statistic, correlation.
- https://stats.libretexts.org/Workbench/Statistics_for_Behavioral_Science_Majors/09%3A_Correlation_and_Regression/9.01%3A_CorrelationCorrelation as a means of measuring the relationship between variables. Subsections cover how to predict correlation from scatterplots of data, and how to perform a hypothesis test to determine if the...Correlation as a means of measuring the relationship between variables. Subsections cover how to predict correlation from scatterplots of data, and how to perform a hypothesis test to determine if there is a statistically significant correlation between the independent and the dependent variables.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Lane)/04%3A_Describing_Bivariate_Data/4.04%3A_Properties_of_rA basic property of Pearson's r is that its possible range is from -1 to 1. A correlation of -1 means a perfect negative linear relationship, a correlation of 0 means no linear relationship, and a cor...A basic property of Pearson's r is that its possible range is from -1 to 1. A correlation of -1 means a perfect negative linear relationship, a correlation of 0 means no linear relationship, and a correlation of 1 means a perfect positive linear relationship.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/13%3A_Introduction_to_Linear_Regression/13.02%3A_Line_Fitting_Residuals_and_CorrelationIn this section, we examine criteria for identifying a linear model and introduce a new statistic, correlation.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Basic_Statistics_Using_R_for_Crime_Analysis_(Choi)/01%3A_Chapters/1.09%3A_CorrelationThis page provides an introduction to correlation, focusing on the Pearson product-moment correlation coefficient, which measures the linear relationship between two variables. It clarifies the miscon...This page provides an introduction to correlation, focusing on the Pearson product-moment correlation coefficient, which measures the linear relationship between two variables. It clarifies the misconception that correlation does not imply causation, explaining that while necessary, correlation alone is not sufficient for causation. The text elaborates on calculating and interpreting Pearson's r, using the USArrests dataset as an example.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/13%3A_Linear_Regression_and_Correlation/13.11%3A_PracticeThis page explores the correlation coefficient (r) in statistics, its calculation, interpretation, and implications for hypothesizing about correlations and regressions. It emphasizes the difference b...This page explores the correlation coefficient (r) in statistics, its calculation, interpretation, and implications for hypothesizing about correlations and regressions. It emphasizes the difference between correlation and causation, and the significance of sample characteristics and data scatter on regression accuracy.
- https://stats.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Ikeda)/08%3A_Describing_Data/8.07%3A_Correlation_and_Causation_Scatter_PlotsThere are many studies that exist that show that two variables are related to one another. The strength of a relationship between two variables is called correlation. Variables that are strongly relat...There are many studies that exist that show that two variables are related to one another. The strength of a relationship between two variables is called correlation. Variables that are strongly related to each other have strong correlation. However, if two variables are correlated it does not mean that one variable caused the other variable to occur.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/07%3A_Correlation_and_Simple_Linear_Regression/7.01%3A_CorrelationIn many studies, we measure more than one variable for each individual. We collect pairs of data and instead of examining each variable separately (univariate data), we want to find ways to describe b...In many studies, we measure more than one variable for each individual. We collect pairs of data and instead of examining each variable separately (univariate data), we want to find ways to describe bivariate data, in which two variables are measured on each subject in our sample. Given such data, we begin by determining if there is a relationship between these two variables. As the values of one variable change, do we see corresponding changes in the other variable?
- https://stats.libretexts.org/Courses/Fort_Hays_State_University/Elements_of_Statistics/08%3A_Linear_Correlation_and_Regression/8.01%3A_Introduction_to_Bivariate_Quantitative_DataIn this chapter we consider bivariate data, which for now consists of two quantitative variables for each individual. Our first interest is in summarizing such data in a way that is analogous to summa...In this chapter we consider bivariate data, which for now consists of two quantitative variables for each individual. Our first interest is in summarizing such data in a way that is analogous to summarizing univariate (single variable) data.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Visual_Statistics_Use_R_(Shipunov)/06%3A_Two-Dimensional_Data_-_Models/6.01%3A_Analysis_of_CorrelationA positive value of means the correlation is positive (the higher the value of one variable, the higher the value of the other), while negative values mean the correlation is negative (the higher the ...A positive value of means the correlation is positive (the higher the value of one variable, the higher the value of the other), while negative values mean the correlation is negative (the higher the value of one, the lower of the other).
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Lane)/10%3A_Estimation/10.11%3A_CorrelationThe computation of a confidence interval on the population value of Pearson's correlation (ρ) is complicated by the fact that the sampling distribution of r is not normally distributed. The...The computation of a confidence interval on the population value of Pearson's correlation (ρ) is complicated by the fact that the sampling distribution of r is not normally distributed. The Z for a 95% confidence interval (Z0.95) is 1.96, as can be found using the normal distribution calculator (setting the shaded area to 0.95 and clicking on the "Between" button).
