Bootstrap estimates confidence intervals for coefficients using resampling. Compare them with large sample methods. Histograms of bootstrap replications show distribution characteristics, aiding comparison. Deviations from normality might indicate differences between bootstrap and large sample confidence intervals.
In statistical analysis, bootstrapping estimates confidence intervals by resampling from the original data. It generates multiple datasets through random sampling with replacement, allowing estimation of coefficient intervals.
Histograms of bootstrapped coefficients display their distributions. Symmetry or skewness in these histograms indicates the distribution shape. If histograms resemble a normal distribution, it implies that the coefficients' bootstrap distributions are approximately normal, supporting traditional methods.
Any deviation from normality in these histograms might suggest discrepancies between the bootstrap and large sample intervals. This comparison helps ascertain the reliability and limitations of both estimation techniques in capturing the true population parameters .
complete the question
7.10.1 Use the bootstrap to estimate confidence intervals for the coeffi cients in the fuel data, and compare the results with the usual large sample ous estimates.
7.10.2 Examine the histograms of the bootstrap replications for each of the coefficients. Are the histograms symmetric or skewed? Do they look like normally distributed data, as they would if the large sample normal theory applied to these data? Do the histograms support or refute the differences between the bootstrap and large sample confidence intervals found in Problem 7.10.17