# Manuals/calci/REGRESSION

REGRESSIONANALYSIS(y,x)

Regression analysis is a form of predictive modelling technique which investigates the relationship between a dependent (target) and independent variable (s) (predictor). This technique is used for forecasting, time series modelling and finding the causal effect relationship between the variables.

• is the set of dependent variables .
• is the set of independent variables.

## Description

• This function is calculating the Regression analysis of the given data.
• This analysis is very useful for the analyzing the large amounts of data and making predictions.
• 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)
```

REGRESSION ANALYSIS OUTPUT

Summary Output
Regression Statistics
Multiple R -0.9989241524588298
R Square 0.9978494623655915
v14193 0.9967741935483871
v15308 0.7071067811865362
ANOVA
Source of Variation Sum Of Squares Degree Of Freedom Mean Of Squares F Significance F
Regression: 464 1 464 928 0.0010758475411702228
Residual: 1 2 0.5
Total: 465 3
ANOVA
Coefficients Standard Error T Statistics Probability Lower 95% Upper 95%
Intercept: 86.5 0.6885767430246738 125.62143708199632 0.00006336233990811291 83.53729339698289 89.46270660301711
X Variable -4 0.13130643285972046 -30.463092423456118 0.0010758475411701829 -4.564965981777541 -3.435034018222459
Residual Output
Observation Predicted Y Residuals Standard Residuals
1 54.5 -0.5 -0.8660254037844387
2 62.5 0.5 0.8660254037844387
3 74.5 0.5 0.8660254037844387
4 82.5 -0.5 -0.8660254037844387

2.

A B C
2 4000 12000 300000
3 5200 13150 411000
4 6800 14090 500000
5 8000 11900 650000
6 10000 15000 800000
1. REGRESSIONANALYSIS(A2:A6,B2:C6)

REGRESSION ANALYSIS OUTPUT

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9973790019059987
R Square 0.9947648734430062
Standard Error 240.4075647503864
Observations 5
ANOVA
df SS MS F Significance F
Regression: 2 21964408.405621577 10982204.202810789 190.0173496501376 0.00523512655699377
Residual: 2 115591.59437842245 57795.797189211225
Total: 4 22080000
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept: -1096.09242 1259.21057 -0.87046 0.47583 -6514.03824 4321.85339 -6514.03824 4321.8533
X Variable1 0.14076 0.10798 1.30359 0.32223 -0.32384 0.60538 -0.32384 0.60538
X Variable2 0.01133 0.00073 15.45951 0.00415 0.00818 0.01449 0.00818 0.01449
Residual Output
Observation Predicted Y Residuals Standard Residuals
1 593.1069112686723 3406.8930887313277 1.5209125615152896
2 754.9885142857306 4445.011485714269 1.9843516155712606
3 887.3091289257611 5912.690871074239 2.6395562126436793
4 579.0302501367541 7420.969749863246 3.312885323147887
5 1015.4067452262161 8984.593254773783 4.010921501026477

REGRESSION