A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since termination of the molding process (x, in hours). Summary quantities include n = 15, SSResid = 1230.848, and SSTo = 24081.642. Calculate the coefficient of determination. (Give the answer to four decimal places.) r2 =

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12-12-2022
Mathematics

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A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since termination of the molding process (x, in hours). Summary quantities include n = 15, SSResid = 1230.848, and SSTo = 24081.642. Calculate the coefficient of determination. (Give the answer to four decimal places.) r2 =

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MOHDFAHAD MOHDFAHAD · Answer 1 · 2022-12-18T09:46:09-05:00

The least-squares approximation can account for 96.95% of the variability in between variables.

Explain the term coefficient of determination?

The effectiveness of a statistical model in forecasting a result is indicated by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.
R² is a more precise measure evaluating goodness of fit. The amount of volatility with in dependent variable which the model can account for.
Even when the correlation is negative, the coefficient of determination has always been positive.

The coefficient of determination could be calculated as follows:

r² = 1 - SS Residual/ SS Total

r² = 1 - 1230.848 / 24081.642.

r² = 1 - 0.0511

r² = 0.94

r = 0.9695

This indicates that the least-squares approximation can account for 96.95 % of a variability between the variables.

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