Manuals/calci/REGRESSIONANALYSIS

REGRESSIONANALYSIS (YRange,XRange,ConfidenceLevel,NewTableFlag)


  • is the set of dependent variables .
  • is the set of independent variables.
  • level of Confidence value.
  • is either 0 or 1.
    • REGRESSIONANALYSIS(), Returns the analysis of numerical data consisting of values of a depeendent and one or more independent variables.

Description

  • This function is calculating the Regression analysis of the given data.
  • The analysis of numerical data consisting of values of a dependent and one or more independent variables
  • This analysis is very useful for the analyzing the large amounts of data and making predictions.
  • Regression analysis is a form of predictive modelling technique which investigates the relationship between a dependent and independent variable.
  • This technique is used for forecasting, time series modelling and finding the causal effect relationship between the variables.
  • This analysis give the result in three table values.
  1. Regression statistics table.
  2. ANOVA table.
  3. Residual output.

1.Regression statistics :

  • It contains multiple R, R Square, Adjusted R Square, Standard Error and observations.
  • R square gives the fitness of the data with the regression line.
  • That value is closer to 1 is the better the regression line fits the data.
  • Standard Error refers to the estimated standard deviation of the error term. It is called the standard error of the regression.

2.ANOVA table:

  • ANOVA is the analysis of variance.
  • This table splits in to two components which is Residual and Regression.
Total sum of squares = Residual (error) sum of squares + Regression (explained) sum of squares. 
  • Also this table gives the probability, T stat, significance of F and P.
  • When the significance of F is < 0.05, then the result for the given data is statistically significant.
  • When the significance of F is > 0.05, then better to stop using this set of independent variables.
  • Then remove a variable with a high P-value and return the regression until Significance F drops below 0.05.
  • So the Significance of P value should be <0.05.
  • This table containing the regression coefficient values also.

3.Residual output:

  • The residuals show you how far away the actual data points are from the predicted data points.

Examples

1.

Spreadsheet
A B
1 Temperature Drying Time(Hrs)
2 54 8
3 63 6
4 75 3
5 82 1
=REGRESSIONANALYSIS(A2:A5,B2:B5,0.65,0)

REGRESSION ANALYSIS OUTPUT

Summary Output
Regression Statistics
Multiple R 0.9989241524588297
R Square 0.9978494623655914
ADJUSTEDRSQUARE 0.996774193548387
STANDARDERROR 0.7071067811865526
OBSERVATIONS 4
ANOVA
DF SS MS F SIGNIFICANCE F
REGRESSION 1 464 464 927.9999999999868 0.001075847541170237
RESIDUAL 2 1.0000000000000142 0.5000000000000071
TOTAL 3 465
COEFFICIENTS STANDARD ERROR T STAT P-VALUE LOWER 95% UPPER 95%
INTERCEPT 86.5 0.6885767430246896 125.62143708199342 0.00006336233990811291 83.53729339698282 89.46270660301718
INDEP1 -4.000000000000007 0.1313064328597235 -30.46309242345547 0.0010758475411701829 -4.564965981777561 -3.4350340182224532


RESIDUAL OUTPUT
OBSERVATION PREDICTED Y RESIDUALS STANDARD RESIDUALS
1 54.49999999999994 -0.49999999999994316 -0.8660254037843341
2 62.49999999999996 0.5000000000000426 0.8660254037845064
3 74.49999999999997 0.5000000000000284 0.8660254037844818
4 82.5 -0.5 -0.8660254037844325

Related Videos

Regression Analysis


See Also

References