Download APPENDIX Regression Output Interpretation_1

APPENDIX Regression Output Interpretation
Ing. Martina Hanová, PhD.
Econometrics I
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0,98
Multiple R: this is the correlation coefficient. It tells you how strong the linear relationship is. For example, a
value of 1 means a perfect positive relationship and a value of zero means no relationship at all. It is the square
root of r squared.
0,96
0,99
R squared: this is R^2, the Coefficient of Determination. It tells you how many points fall on the regression line.
for example, 80% means that 80% of the variation of y-values around the mean are explained by the x-values. In
other words, 80% of the values fit the model.
Adjusted R square
Standard Error of the regression: An estimate of the standard deviation of the error μ. This is not the same as
the standard error in descriptive statistics! The standard error of the regression is the precision that the
regression coefficient is measured; if the coefficient is large compared to the standard error, then the coefficient
is probably different from 0.
Observations: Number of observations in the sample.
20,8
15
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
1
13
14
Coefficients
-184,07
0,71
SS
MS
F
3351406,528 3351406,5 8144,5339
5349,389603 411,49151
3356755,917
Standard Error
46,262
0,008
t Stat
-3,98
90,25
P-value
0,001573
1,42E-19
Significance F
1,42044E-19
Lower 95%
-284,021
0,689
Upper 95%
-84,135
0,723
Linear regression equation
y = intercept + slope * x
y = -184,07 + 0,71* x
Intercept
Slope
often labeled the constant, is the expected mean value of Y when X=0, y-axis intercept of the regression line.
also called the regression coefficient, the expected mean value change of Y for a one unit increase in X.