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- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/12%3A_Variance_Covariance_and_Linear_Regression/12.01%3A_Variancejdemo1 % Call for data jcalc % Set up Enter JOINT PROBABILITIES (as on the plane) P Enter row matrix of VALUES of X X Enter row matrix of VALUES of Y Y Use array operations on matrices X, Y, PX, PY, t...jdemo1 % Call for data jcalc % Set up Enter JOINT PROBABILITIES (as on the plane) P Enter row matrix of VALUES of X X Enter row matrix of VALUES of Y Y Use array operations on matrices X, Y, PX, PY, t, u, and P G = t.^2 + 2*t.*u - 3*u; % calcculation of matrix of [g(t_i, u_j)] EG = total(G.*P) % Direct calculation of E[g(X,Y)] EG = 3.2529 VG = total(G.^.*P) - EG^2 % Direct calculation of Var[g(X,Y)] VG = 80.2133 [Z,PZ] = csort(G,P); % Determination of distribution for Z EZ = Z*PZ' % E[Z] from d…
- https://stats.libretexts.org/Courses/Rio_Hondo_College/PSY_190%3A_Statistics_for_the_Behavioral_Sciences/13%3A_Correlations/13.01%3A_Variability_and_CovarianceBecause we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score chan...Because we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score changes, does the other score also change in a predictable or consistent way? This notion of variables differing together is called covariance (the prefix “co” meaning “together”).
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/12%3A_Variance_Covariance_and_Linear_Regression/12.02%3A_Covariance_and_the_Correlation_CoefficientReference to Figure 12.2.1 shows this is the average of the square of the distances of the points \((r, s) = (X^*, Y^*) (\omega)\) from the line \(s = r\) (i.e. \(1 - \rho\) is proportional to the var...Reference to Figure 12.2.1 shows this is the average of the square of the distances of the points \((r, s) = (X^*, Y^*) (\omega)\) from the line \(s = r\) (i.e. \(1 - \rho\) is proportional to the variance abut the \(\rho = 1\) line and \(1 + \rho\) is proportional to the variance about the \(\rho = -1\) line. \(\rho = 0\) iff the variances about both are the same.
- https://stats.libretexts.org/Courses/Sacramento_City_Colllege/PSYC_330%3A_Statistics_for_the_Behavioral_Sciences_with_Dr._DeSouza/14%3A_Correlations/14.01%3A_Variability_and_CovarianceBecause we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score chan...Because we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score changes, does the other score also change in a predictable or consistent way? This notion of variables differing together is called covariance (the prefix “co” meaning “together”).
- https://stats.libretexts.org/Courses/Taft_College/PSYC_2200%3A_Elementary_Statistics_for_Behavioral_and_Social_Sciences_(Oja)/03%3A_Relationships/14%3A_Correlations/14.06%3A_Correlation_Formula-__Covariance_Divided_by_VariabilityNow that you know more about what Pearson's correlation means, let's look at the actual formula.
- 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/Applied_Statistics/An_Introduction_to_Psychological_Statistics_(Foster_et_al.)/12%3A_Correlations/12.01%3A_Variability_and_CovarianceBecause we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score chan...Because we have two continuous variables, we will have two characteristics or score on which people will vary. What we want to know is do people vary on the scores together. That is, as one score changes, does the other score also change in a predictable or consistent way? This notion of variables differing together is called covariance (the prefix “co” meaning “together”).
- https://stats.libretexts.org/Workbench/PSYC_2200%3A_Elementary_Statistics_for_Behavioral_and_Social_Science_(Oja)_WITHOUT_UNITS/14%3A_Correlations/14.06%3A_Correlation_Formula-__Covariance_Divided_by_VariabilityNow that you know more about what Pearson's correlation means, let's look at the actual formula.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Biological_Statistics_(McDonald)/05%3A_Tests_for_Multiple_Measurement_Variables/5.04%3A_Analysis_of_CovarianceUse analysis of covariance (ancova) when you have two measurement variables and one nominal variable. The nominal variable divides the regressions into two or more sets.
