Construction of multivariable demand function Testing and evaluation

Construction of multivariable demand function Testing and evaluation of multivariable demand function 1

Step 1. Testing the suitability of the model Signs of the coefficients Parameter values 2

The 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 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 3 Root-mean-square error of regression coef. Dispersion analysis sum of squares coefficient of determination Root-mean-square error of regression

Parameter 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? 4

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^2 5 I'm still waiting for the day when I will need to know the solution of in real life

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 data 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 6

SSR 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 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 7 Dispersion analysis sum of squares coefficient of determination

Step 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 parameters number of observations The number of independent variables 8 To get useful results, the number of observations should be sufficient 8

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 9

Step 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 ^ 10

0,009 11 Root-mean-square error of regression