Definitions of Important
Univariate and Bivariate Statistics

Mean of variable x:
Residual Sum of Squares in x:
Residuals Sum of Squares in y ("Total Variance"):
Residuals Sum of Squares in x, y cross product:
Unbiased sample variance:
Correlation
Parametric
(Pearson's) correlation coefficient:
Non-Parametric:
Spearman's rank correlation coefficient:
Statistics of a least squares line
( y = a + bx  )
The slope (b):


    Notice that the slope "b" of the line is equal to the correlation
    coefficient scaled by the standard deviations in y and x.

 

The intercept (a):
Total Variance:
Residual Sum of Squares of the Linear Regression Model:

Coefficient of Determination ("Variance Explained"):
    Question: Where have you see this before?

Standard Deviation (or RMSE):
Confidence interval on the slope m:
    Note that t-crit is the critical t-value for a user selected

    alpha value with df = (n - 2)and were

    the standard deviation of the slope is defined as:

 

Confidence interval for the regression line:

 

   Note that t-crit is the critical t-value for a user selected

   alpha value with df = (n - 2)and were

   the standard deviation of the line is defined as:

 

Confidence interval for individual model predictions, y-hat:

 

   Note that t-crit is the critical t-value for a user selected

   alpha value with df = (n - 2)and were

   the standard deviation of the individual model prediction y-hat is defined as: