Consider a simple linear regression model with one predictor variable X and one response variable Y. The regression equation is given by Y = β0 + β1X, where β0 and β1 are the intercept and slope coefficients, respectively. The sample size is n = 100 and the coefficient of determination (R^2) for the model is 0.25. What can we conclude about the strength of the relationship between X and Y?

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Consider a simple linear regression model with one predictor variable X and one response variable Y. The regression equation is given by Y = β0 + β1X, where β0 and β1 are the intercept and slope coefficients, respectively. The sample size is n = 100 and the coefficient of determination (R^2) for the model is 0.25. What can we conclude about the strength of the relationship between X and Y?
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A coefficient of determination (R^2) of 0.25 means that 25% of the variance in the response variable Y can be explained by the predictor variable X. So, we can conclude that there is a weak linear relationship between X and Y in the population.

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