A survey contains the following questions:

• Question 0: How satisfied are you with our company?
• Question 1: How satisfied are you with service?
• Question 2: How satisfied are you with the products?

The possible answers for each question fall into the following range:

• 1 (very satisfied): Valuation 100
• 2 (satisfied): Valuation 80
• 3 (mixed opinion, tending towards satisfied): Valuation 60
• 4 (mixed opinion, tending towards dissatisfied): Valuation 40
• 5 (dissatisfied): Valuation 20
• 6 (very dissatisfied): Valuation 0
• No answer given: no valuation possible

Customers return the following results:

Linear regression expresses for the addressed customers the relationship between their answers to question 0 and their answers to questions 1 and 2 (equation A):

Answer (question 0) = constant + a_1 * answer (question 1) + a_2 * answer (question 2)

The equation can be expressed more generally as follows:

y = a0 + a1 * x1+ a2 * x2 + …

The regression coefficients a1 and a2 are determined in such a way that all answers for question 0 have a minimum standard variance to the answers to question 0 calculated on the right-hand side of equation A.

Let us assume that the calculation for the above survey yields the following results:

• a0 = 0.20
• a1 = 0.20
• a2 = 0.60

The standardized regression coefficient, called "importance", is corrected by its own standard variances and the standard variance of x0:

a' = a * standard variance (x) / standard variance (y)

If, for example, the result below is obtained, then it means that the overall satisfaction (question 0) is mainly determined by question 2. Question 1 is only half as important as question 2.

• a1' = 0.40
• a2' = 0.80

The first value that returns the meaningfulness of the results is the standard error that expresses the relationship between the answers received for question 0 and the calculated answers (right-hand side of equation A).

Possible results:

• Mean value of the valuation for question 0: 82.0
• Standard error: 4.1

This is interpreted as a standard error of 5%, which means that the calculation contains a high level of inaccuracy.

If the calculated F test returns a significance of over 0.95, then the calculated regression coefficients show with 95% significance a meaningful relationship between question 0 on the one side and questions 1 and 2 on the other side.

Possible results of the T tests:

• a1: Significance 0.90
• a2: Significance 0.99

In the same way as the F test, the T test for the individual regression coefficients describes the significance of a meaningful relationship between y and the respective x parameter. In the example used here, a2 obtains a high significance value whereas that obtained by a1 is too low. In cases where significance falls below 95%, it is advisable to check the meaningfulness of the results with another customer group.