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Construction of multivariable demand function Testing and evaluation of
Содержание
- 1. Construction of multivariable demand function Testing and evaluation of
- 2. Step 1. Testing the suitability of the modelSigns of the coefficientsParameter values
- 3. The positive sign:The negative sign:The demand variable
- 4. Parameter valuesThis is parameter validation on economic
- 5. Corrected plural coefficient of determination, R^2Root-mean-square
- 6. Plural coefficient of determination, R^2Step 2.
- 7. SSR Explainable variation SSЕ Unexplained variationSSТ Full
- 8. Step 2. Statistical tests and evaluation Corrected
- 9. Acceptable values of
- 10. Step 2. Statistical tests and evaluation Root-mean-square
- 11. 0,009 Root-mean-square error of regression
- 12. Скачать презентанцию
Step 1. Testing the suitability of the modelSigns of the coefficientsParameter values
Слайды и текст этой презентации
Слайд 1Construction of multivariable demand function
Testing and evaluation of multivariable demand
function
Слайд 3The positive sign:
The negative sign:
The demand variable and the independent
variable are changing in opposite directions
Demand Variable changes in the
same direction as the independent variableThe sign of the parameter indicates the direction of change of the demand variable with respect to changes in the independent variable
0,009
Variable №
Are marks of b1 and b2 consistent with the theory?
Q = 3,45 + 0,5 X1 + 0,009 X2
Quantity of prospective consumers (1000)
Income per capita
Root-mean-square error of regression coef.
Dispersion analysis
sum of squares
coefficient of determination
Root-mean-square error of regression
Слайд 4Parameter values
This is parameter validation on economic sense
The generally accepted
limits do not exist, but most economists subjectively limit values
of each parameter] aggregate demand = a function of prices and disposable income:
Cd = b0 + b1 X1 + b2 X2
] b1 = 2 b2 = 1,3
In accordance with b2, the consumer must spend 1,3 $ per each additional 1$ income
Do these parameters have sense?
Слайд 5 Corrected plural coefficient of determination, R^2
Root-mean-square error of estimation
for the regression
Step 2. Statistical tests and evaluation
Common tests
Plural
coefficient of determination, R^2I'm still waiting for the day when I will need to know the solution of
in real life
Слайд 6 Plural coefficient of determination, R^2
Step 2. Statistical tests and
evaluation
Is a measure of how well the plane described by
the regression equation, satisfies the experimental dataFull variation = Explainable variation + Unexplained variation
Variation is the sum of the squared deviations of observed values from the regression line
^
^
R^2 = Explainable variation /Full variation =
^
Multiple regression describes the regression plane and the observed points lie above, below, and on this plane
The factor has only mathematical sense and does not determine any causal relationships
Слайд 7SSR Explainable variation
SSЕ Unexplained variation
SSТ Full variation
This means
that 99.89 per cent changes in sales are explained by
changes in the size of the target population and per capita incomeR^2 = 0 – there is no relationship between demand and other variables
R^2 = 1 –all changes in demand are explained by simultaneous changes of the independent variables
0 < R^2 < 1
0,009
Dispersion analysis
sum of squares
coefficient of determination
Слайд 8Step 2. Statistical tests and evaluation
Corrected plural coefficient of
determination, R^2
Pays due attention to the degrees of freedom determined
by the number of observations and number of parametersnumber of observations
The number of independent variables
8
To get useful results, the number of observations should be sufficient
Слайд 9 Acceptable values of
?
Usually if the number of observations is three or four
times more than the number of independent variables, it is considered that acceptable value is
Слайд 10Step 2. Statistical tests and evaluation
Root-mean-square error of estimation
for the regression
Characterizes the dispersion of the observed points from
the theoretical regression line (determines the random scatter of the observed values of Q, relative to the estimated values of Q)^
Root-mean-square error of estimation
The observed value of the dependent demand variable in the i-th point
Estimated value of the dependent demand variable, calculated for the i-th point on the regression equation
The number of independent variables
^
