STATA Application and Statistical Analysis

Extract

[...] We want to test if the mortality rate is higher in urban areas - that is, to check if the estimated coefficient for the variable purban is positive, or at least different from zero. We can use the test function on Stata after the regression, with: regress fatrate percapdisp purban regist rmiles intermiles test purban=0 The results displayed on the console give the Fisher statistic with 45 degrees of freedom (51 data points - 6 variables) of 3.18. The p-value is 8.15%, which is greater than 5%. [...]

[...] and standard deviation then we know that 95% of the possible values are within the interval By adopting the values of the random sample, the confidence interval for ? would therefore be: where X and s are the sample values, and n its size (n=400) the 95% confidence interval will therefore be: [355,8355; 359,6245] Given that the two values (mean and standard deviation) are unknown, we use a Student's t-test to verify the null hypothesis H0=350. To test this hypothesis, we calculate the Student's t-statistic as follows: so it t = 4.081. [...]

[...] On deduce that the estimatoris more efficient. Ambiguous question. Question 2 Based on the data, the sample variance is written as: where X is the mean of the sample. So: V(X)=993.27 We know that the confidence interval of a variance is expressed as follows:where ? is the confidence threshold a Chi-2 distribution with n-1 degrees of freedom and s2 the sample variance. Therefore, the confidence interval of the variance will be: [494,263 ; 3208,007] One tests H0 : ?2=500 at the 10% threshold. [...]

[...] The first column (Coef.) reports the estimated value, its standard deviation, as well as the Student statistic, the p-value, and finally the confidence interval for the estimator. Finally, the last line in this table, _cons represents the constant In order to determine which variables are statistically significant, it is sufficient to observe the p-values (the P>t column): values below are retained accordingly. In our case, the wealth per capita is the only significant explanatory variable at since all other variables have p-values above. [...]

[...] An unbiased estimator, denoted ? is unbiased if where ? is the theoretical value. est equal to the value drawn from X1, don't my mean is However, given that it's a sample draw, the empirical mean is calculated as follows: On average, therefore, we should expect that The estimator is therefore unbiased. Nevertheless, the definition of an unbiased estimator allows it to be defined as where the bias is now written Similarly, we have: so in average also, we should expect to The most efficient estimator will be the one with the lowest variance. [...]