# 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.

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
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

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Regression Analysis