Practical Econometrics

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Economist, studying the dependence of the level of distribution costs at the (thous.) Of the volume of trade turnover x (thous.), Examined 10 shops selling the same range of products in different regions. The data obtained are shown in Table 1 number.

X 80 60 100 130 120 50 90 150 70 125
At 4.2 4.9 7.2 9.1 6.4 3.9 5.1 8.4 3.5 8.7

According to the table for your option, perform the following tasks.

Task 1. Draw a point scatterplot and form a hypothesis about the form of communication.

Task 2. Determine the parameters of the linear regression function and record a linear relationship.

Task 3. Plot the regression on the scatterplot and draw a conclusion about the adequacy of the constructed model.
Task 4.
Find the correlation coefficient and the coefficient of determination of this dependence. Confirm whether the conclusions about the form of communication and the adequacy of the model.
Task 5.
Determine the reliability of the regression coefficients by Student's test.

Test the hypothesis H0 of equality of the individual regression coefficients to zero (if not equal to the alternative H1) at a significance level α = 0.05.
If the basic hypothesis would be false, we accept the alternative. To test this hypothesis using the Student's t-test.
Found on observational data value t-test (also known as the observed or actual) is compared with tabulated (critical) value, determined by the table of Student's distribution (which are usually given at the end of books and workshops on statistics or econometrics).
Table value is determined by the level of significance (α) and the number of degrees of freedom, which in the case of linear regression of the pair is equal to (n-2), n-number of observations.
If the actual value of the t-test large table (in absolute value), then reject the null hypothesis and believe that with probability (1-α) setting or the statistical characteristics in the population is significantly different from zero.
If the actual value is less than the t-test table (in absolute value), then there is no reason to reject the null hypothesis, ie, statistical parameter or characteristic in the population not significantly different from zero at a significance level α.
tkrit (nm-1; α / 2) = (8; 0.025) = 2.306
Task 6.
Explore the regression on the reliability of the Fisher test at a significance level of 0.05.

Testing the significance of the regression model is carried out using F-Fisher criterion, the estimated value of which is the ratio of the variance of the original series of observations studied indicator and unbiased estimates of the variance of the residual sequence for this model.
If the calculated value k1 = (m) and k2 = (nm-1) degrees of freedom over the table at a given significance level, then the model is considered significant
Task 7.
Find the coefficient of elasticity in respect to x, with an average value of x.

The average coefficient of elasticity E shows the percentage of the average aggregate result from changes from its average value when changing the x factor 1% of its average value.
The coefficient of elasticity is given by
Task 8.
Calculate the average value of the expected costs of turnover of 115 thousand. Rub.
Task 9.
Rate the forecast error at a significance level of 0.05.

We calculate the limit of the range, which will focus 95% of the possible values \u200b\u200bof Y at an infinitely large number of observations and Xp = 115
Task 10.
Build confidence intervals for the forecast of the significance level of 0.05.


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