Testing and evaluation of multivariable demand function презентация

values

are changing in opposite directions

Demand Variable changes in the same direction as the independent variable

The 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

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?

the regression

Step 2. Statistical tests and evaluation

Common tests

Plural coefficient of determination, R^2

I'm still waiting for the day when I will need to know the solution of

in real life

a measure of how well the plane described by the regression equation, satisfies the experimental data

Full variation = Explainable variation + Unexplained variation

Variation is the sum of the squared deviations of observed values from the regression line

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R^2 = Explainable variation /Full variation =

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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

99.89 per cent changes in sales are explained by changes in the size of the target population and per capita income

R^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

R^2

Pays due attention to the degrees of freedom determined by the number of observations and number of parameters

number of observations

The number of independent variables

8

To get useful results, the number of observations should be sufficient

if the number of observations is three or four times more than the number of independent variables, it is considered that acceptable value is

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)

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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

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