Regression functions

expression1

An expression that returns a value of any built-in numeric, character-string, or graphic-string data type. If the argument is a character-string or graphic-string, it is cast to DECFLOAT(34) before evaluating the function.

expression2

An expression that returns a value of any built-in numeric, character-string, or graphic-string data type. If the argument is a character-string or graphic-string, it is cast to DECFLOAT(34) before evaluating the function.

The REGR_COUNT function returns the number of non-null number pairs used to fit the regression line.

The REGR_INTERCEPT function returns the y-intercept of the regression line ("b" in the equation y = a * x + b).

The REGR_R2 function returns the coefficient of determination ("R-squared" or "goodness-of-fit") for the regression.

The REGR_SLOPE function returns the slope of the line ("a" in the equation y = a * x + b).

The REGR_AVGX, REGR_AVGY, REGR_SXX, REGR_SXY, and REGR_SYY functions return quantities that can be used to compute various diagnostic statistics needed for the evaluation of the quality and statistical validity of the regression model.

The data type of the result of REGR_COUNT is bigint. For the remaining functions, if either argument is DECFLOAT(n), the data type of the result is DECFLOAT(34); otherwise, the data type of the result is double-precision floating-point. If either argument is a special decimal floating-point value, the rules for general arithmetic operations for decimal floating-point apply. See General arithmetic operation rules for DECFLOAT for more information.

The result can be null. When not null, the result of REGR_R2 is between 0 and 1, and the result of both REGR_SXX and REGR_SYY is non-negative.

Each function is applied to the set of (expression1, expression2) pairs derived from the argument values by the elimination of all pairs for which either expression1 or expression2 is null.

If the set is empty, REGR_COUNT returns zero and the remaining functions return a null value.

If the set is not empty, the functions return results defined as follows:

REGR_COUNT

The number of non-null pairs in the set

REGR_SLOPE

If VARIANCE(expression2) is positive:

  REGR_SLOPE(expression1,expression2) =
      COVARIANCE(expression1,expression2)/VARIANCE(expression2)

If VARIANCE(expression2) is equal to zero, returns the null value.

REGR_INTERCEPT

If VARIANCE(expression2) is positive:

  REGR_INTERCEPT(expression1, expression2) =
      AVG(expression1) - REGR_SLOPE(expression1, expression2) * AVG(expression2)

If VARIANCE(expression2) is equal to zero, returns the null value.

REGR_R2

If VARIANCE(expression2) is positive:

• If VARIANCE(expression1) is positive:

    REGR_R2(expression1, expression2) =
        POWER(CORRELATION(expression1, expression2), 2)

• if VARIANCE(expression1) is equal to zero:

    REGR_R2(expression1, expression2) = 1 
  

If VARIANCE(expression2) is equal to zero, returns the null value.

REGR_AVGX

REGR_AVGX(expression1, expression2) = AVG(expression2)

REGR_AVGY

REGR_AVGY(expression1, expression2) = AVG(expression1)

REGR_SXX

REGR_SXX(expression1, expression2) =
      REGR_COUNT(expression1, expression2) * VARIANCE(expression2)

REGR_SYY

REGR_SYY(expression1, expression2) =
      REGR_COUNT(expression1, expression2) * VARIANCE(expression1)

REGR_SXY

REGR_SXY(expression1, expression2) =
      REGR_COUNT(expression1, expression2) * COVARIANCE(expression1, expression2)

The order in which the values are aggregated is undefined, but every intermediate result must be within the range of the result data type.

The usual diagnostic statistics that accompany a linear-regression analysis can be computed in terms of the above functions. For example:

    Adjusted R2
        1 - ( (1 - REGR_R2) * ((REGR_COUNT - 1) / (REGR_COUNT - 2)) )
    Standard error
        SQRT( (REGR_SYY-(POWER(REGR_SXY,2)/REGR_SXX))/(REGR_COUNT-2) )
    Total sum of squares
        REGR_SYY
    Regression sum of squares
        POWER(REGR_SXY,2) / REGR_SXX
    Residual sum of squares
        (Total sum of squares)-(Regression sum of squares)
    t statistic for slope
        REGR_SLOPE * SQRT(REGR_SXX) / (Standard error)
    t statistic for y-intercept
       REGR_INTERCEPT/((Standard error) * 
          SQRT((1/REGR_COUNT)+(POWER(REGR_AVGX,2)/REGR_SXX)))