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If the points on a scatter diagram seem to be best described by a curving line, which one of the regression assumptions might be violated?

Answer :

Final answer:

The regression assumption that would be violated if a curving line best describes the scatter plots is the assumption of linearity. This means that there isn't a straight-line relationship between the variables and a different model might be needed to describe the data effectively.

Explanation:

Regression assumptions are key for reaching valid conclusions from your regression analysis. In the situation where the points on a scatter diagram seem to be best described by a curving line, this would violate the regression assumption of linearity. Linearity assumes that there is a straight-line relationship between your predictor and response variables. If your scatter plot indicates a curve, this assumption is violated, and a linear model might not be suitable for your data.

For example, if you were plotting a person's height (the dependent variable, y) against the length of their pinky finger (the independent variable, x), you might see a pattern that a curving line would describe more effectively than a straight line. In such cases, one might need to explore other methods to fit curves to the data, such as polynomial regression or transformation of the data.

Examining the scatter plot and testing the significance of the correlation coefficient, as well as checking the residuals and their distribution, helps us determine whether the linearity assumption holds, or if it's violated, as in this case.

Learn more about Linearity Violation here:

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