Question

Which of the following statements is true?

a. non-linear regression relationships can be estimated using non-linear forms such as polynomials, exponentials or logarithms.
b. it is impossible to fit a regression line to non-linear data.
c. regression analysis is seldom used by statisticians for business applications.
d. unless a regression produces a coefficient of determination of 1 (or -1), the estimated equation is useless.

Answer 1

The true statement is that non-linear regression relationships can be estimated using non-linear forms such as polynomials, exponentials, or logarithms. Regression analysis can handle non-linear data using various models, and it is a commonly used statistical tool in business and other fields. Therefore, the correct option is a).

Step-by-step explanation:

The question revolves around the concept of regression analysis, specifically linear and non-linear regression. A correct understanding of this statistical concept is important for analyzing various types of data. Out of the options provided in the question, the true statement is 'Non-linear regression relationships can be estimated using non-linear forms such as polynomials, exponentials or logarithms.'

This refers to the ability of regression analysis to fit models to data that do not follow a straight line, and this can include forms that have a curved relationship such as quadratic, exponential, and inverse relationships as presented in the reference figures. Contrary to the incorrect options, it is indeed possible to fit regression models to non-linear data, statisticians frequently utilize regression analysis for business applications, and a coefficient of determination (R-squared value) less than 1 does not render an estimated regression equation useless; it simply means the model does not explain 100% of the variance in the dependent variable.