In order to build a confidence interval we utilize the standard error of the estimate, S_e, which measures the dispersion of the dependent variable from the regression line. For any given set of independent variables, we can calculate an estimated dependent variable value, assuming a normal distribution of error terms.

For example, in our Mrs. Jelinek’s Pie Company regression equation is Q_x = 42,909.77 – 32.549P_x with a standard error of the estimate of 1,663. If we want to know with 95% confidence what Q_x will be if P_x = 600 cents, we first calculate the predicted Q_x = 23,380.37.

From the properties of a normal distribution, we will also know that there is a 68% probability that the actual value for Q_x will lie within one standard error of the predicted value, and a 95% probability that it will lie within two standard errors of the predicted value.

So we add two standard errors (2 times 1,663) to the predicted value 23,380.37 and subtract two standard errors from this value to get a 95% confidence interval 20,054.37< Q_x < 27,706.37.

In conclusion, when the pie price is 600 cents a pie, our best estimate of sales is 23,380.37 pies. However, we don’t really expect the actual sales to fall at exactly that number because the estimate is derived from data that exhibited deviations from the line of best fit. Thus we can be confident at the 95% level that when the price is set at 600 cents, sales will fall within the range 20,054.37 units to 27,706.37 units. Clearly, we would prefer to discover a smaller standard error of the estimate, since the confidence interval would then be smaller and we could be more confident of experiencing an actual level of sales closer to the expected level of sales.