Question

Chapter 4, Example 13

Nodel's VP of operations now wants to know the error associated with the regression line computed in Example 12.

I calculated the standard error of the estimate to be $306,000 in sales. This is Chapter 4, Example 13 in the book.

The interpretation of the standard error of the estimate is similar to the standard deviation: namely, +- standard deviation = .6827. So there is a 68.27% chance of sales being +- $306000 from the point estimate of $3,250,000. I don't understand where the .6827 came from?

Answer 1

Here The mean sales are $3250000 and the distribution of sales estimate follows a normal distribution. The standard error of estimate implies the limits of confidence that the chance of sales +- $306000. One standard error limit signifies 1 Standard deviation (σ ) limit i.e. 68.27%.

In a normal distribution, this is known as 68 - 95 - 99.7 rule or three-sigma rule where 1 standard deviation ( 1 σ) means 68.27% of sales estimate values lie within +- $306000.

μ ± σ i.e. 68.27% of sales estimate values lie within +- $306000.

μ ± 2σ i.e. 95.45% of sales estimate values lie within +- 2 * $306000.

μ ± 3σ i.e. 99.73% of sales estimate values lie within +- 3 * $306000.

The .6827 comes from the 3-sigma rule established in standard normal distribution.