Confidence interval for individual coefficients

The values of obtained by estimating model (1) using sample data give the point estimates of , respectively, which are the population parameters. Using the values of the sample statistics , we can make confidence intervals for the corresponding population parameters ,

respectively.

If the population errors, , are normally distributed, then confidence interval for the regression coefficients , are given by

where is the number for which

and the random variable follows a Student’s t distribution with degrees of freedom.

Example:

Determine a 90% confidence interval for (the coefficient of experience) for the multiple regression of auto insurance premium on driving experience and the number of driving violations. Use the MINITAB solution of Fig. 4.1.

Solution:

The portion of the solution is shown below

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