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.
- Regression statistics table.
- ANOVA table.
- 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
Regression Statistics | |
---|---|
Multiple R | -0.9989241524588298 |
R Square | 0.9978494623655915 |
v14193 | 0.9967741935483871 |
v15308 | 0.7071067811865362 |
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 |
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 |
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 | |
---|---|---|---|
1 | Unit sales | Ads | population |
2 | 4000 | 12000 | 300000 |
3 | 5200 | 13150 | 411000 |
4 | 6800 | 14090 | 500000 |
5 | 8000 | 11900 | 650000 |
6 | 10000 | 15000 | 800000 |
- REGRESSIONANALYSIS(A2:A6,B2:C6)
REGRESSION ANALYSIS OUTPUT
Regression Statistics | |
---|---|
Multiple R | 0.9973790019059987 |
R Square | 0.9947648734430062 |
Adjusted R Square | 0.9895297468860125 |
Standard Error | 240.4075647503864 |
Observations | 5 |
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 |
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 |
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