In the context of linear regression and the least squares method, what is the primary purpose of regression analysis?

• A. To prove that two variables have a causal relationship whenever their correlation is nonzero
• B. To compute the median of a response variable separately for each level of a categorical predictor
• C. To eliminate all random error from observed data by forcing every point to lie exactly on a fitted line
• D. To model and quantify the relationship between a response variable and one or more predictor variables for purposes such as prediction and explanation

Answer: (D)

Verified step by step guidance

1. Understand that regression analysis is a statistical method used to examine the relationship between variables, specifically between a response (dependent) variable and one or more predictor (independent) variables.
2. Recognize that the least squares method is a technique used in regression to find the best-fitting line by minimizing the sum of the squared differences (errors) between observed values and the values predicted by the model.
3. Note that the primary goal of regression is not to prove causation, but to model and quantify the strength and form of the relationship, which can be used for prediction and explanation.
4. Acknowledge that regression does not eliminate all random error; instead, it accounts for variability by fitting a line that best represents the trend in the data, allowing for some residual error.
5. Conclude that regression analysis helps in understanding how changes in predictor variables are associated with changes in the response variable, which is essential for making informed predictions and explanations.