Linear regression model

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Researchers suggested that the value of the carbon isotope δ13C in human serum might reflect dietary consumption of corn‐based and cane‐based sweeteners. This might then offer a measure that objectively reflects intake of sweets and could thus replace unreliable self‐reported dietary assessments. They investigated this possibility among a sample of 186 participants by using a linear regression model with the level of δ13C in serum as the outcome variable and the level of the consumption of sweetened drinks (estimated number of cans consumed per day) as the covariate. They then successively added to the basic model: first, corn consumption then male gender and then consumption of animal fat (% total calories/day). For each model, they measured R2 (described in output as “Adjusted r‐squared value”). The results are shown in Figure 22.15. Comment on what these successive R2 values suggest about goodness‐of‐ fit for each addition to the simple model.

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