Manuals/calci/REGRESSIONANALYSIS

REGRESSIONANALYSIS (YRange,XRange,ConfidenceLevel,NewTableFlag)

• $YRange$ is the set of dependent variables .
• $XRange$ is the set of independent variables.
• $ConfidenceLevel$ level of Confidence value.
• $NewTableFlag$ 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

See Also

• SLOPE
• STEYX

References

• Regression Analysis

• List of Main Z Functions

• Z3 home