Final answer:
The statement is false. Multiple regression can identify relationships but cannot on its own prove causality due to the possibility of confounding factors and the fundamental correlation-causation fallacy in statistical analysis.
Step-by-step explanation:
The statement that multiple regression enables the researcher to show that two variables are causally related is false. Multiple regression analysis can indeed identify relationships between a dependent variable and multiple independent variables, allowing researchers to examine the influence of various factors on an outcome. For instance, in studying obesity within neighborhoods, researchers could consider the number of fast food joints, ethnicity, income, access to parks, etc. However, it's imperative to understand that correlation, as identified by regression analysis, does not imply causality. There may be confounding variables that affect the variables of interest, creating a correlation that does not reflect a direct cause-and-effect relationship.
For example, a positive correlation between variables simply indicates that as one variable increases, the other tends to increase as well. This does not mean there are health benefits associated with the variable under investigation. To truly establish causality, controlled experiments or additional statistical techniques beyond correlation are often necessary, sometimes involving a control group to account for extraneous factors.
In essence, while regression can provide important clues about potential relationships between variables and can help in predictive modeling, it does not, on its own, demonstrate causality. Additional research and methods are required to draw conclusions about cause and effect. The concept that correlation does not imply causation is a fundamental principle in statistical analysis and research methodology and is known as the correlation-causation fallacy.