Choose all that apply when describing R^2. (Select all that apply.) Is used to determine the fit of a model. Can be inflated by adding more variables. Only describes the relationship between quantitative variables. Represents the percent of variability in y that can be explained by the model. Is only used in multiple linear regression. In simple linear regression, it is equal to the correlation coefficient r^2. Referred to as the coefficient of determination or coefficient of multiple determination. Can be inflated by removing variables.

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09-12-2022
Mathematics

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Choose all that apply when describing R^2. (Select all that apply.) Is used to determine the fit of a model. Can be inflated by adding more variables. Only describes the relationship between quantitative variables. Represents the percent of variability in y that can be explained by the model. Is only used in multiple linear regression. In simple linear regression, it is equal to the correlation coefficient r^2. Referred to as the coefficient of determination or coefficient of multiple determination. Can be inflated by removing variables.

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KalpanaDalal KalpanaDalal · Answer 1 · 2022-12-16T09:36:33-05:00

The following statements are correct,

a.) Is used to determine the fit of a model.

b.) Can be inflated by adding more variables.

c.) Referred to as the coefficient of determination

d.) Represents the percent of variability in y that can be explained by the model.

e.) In simple linear regression, it is equal to the correlation coefficient r².

Define Regression Analysis

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

R² ≡ 1 - SS(res) / SS(tot)

SS(res) + SS(reg) = SS(tot)

R² = SS(reg) / SS(tot) = (SS(reg)/n) / ( SS(tot)/n )

Where,

The total sum of squares(proportional to the variance of the data),

SS(tot) = ∑ (y - y(bar) )₂

The regression sum of squares, also called the explained sum of squares,

SS(reg) = ∑ (f(i) - y(bar) )²

The sum of squares of residuals, also called the residual sum of squares,

SS(res) = ∑ (y(i) - f(i) )² = ∑e²(i)

To read more about Regression Analysis.

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