Construction of multivariable demand function Testing and evaluation of

function

coefficients
Parameter values

variable are changing in opposite directions
Demand Variable changes in the

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

limits do not exist, but most economists subjectively limit values

] 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?

for the regression

Step 2. Statistical tests and evaluation
Common tests
Plural

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

in real life

evaluation
Is a measure of how well the plane described by

Full 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

that 99.89 per cent changes in sales are explained by

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

determination, R^2
Pays due attention to the degrees of freedom determined

number of observations

The number of independent variables

8

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

?
Usually if the number of observations is three or four

for the regression

Characterizes the dispersion of the observed points from

^

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

^