Question

The following estimated regression equation based on 30 observations was presented. y=17.6+3.8x₁​−2.3x₂​+7.6x₃​+2.7x₄​ The values of SSt and SSR are 1,809 and 1,750, respectively. Compute A². (Round your answer to three decimal places.) R²=?

Answer 1

To compute the coefficient of determination (R²), divide SSR (1,750) by SSt (1,809) and round the result to three decimal places. R² indicates how much of the variability in y is explained by the regression model.

Step-by-step explanation:

The given regression equation is y=17.6+3.8x₁​−2.3x₂​+7.6x₃​+2.7x₄ and you have been provided with the total sum of squares (SSt) and the sum of squares due to regression (SSR) being 1,809 and 1,750 respectively. To compute the coefficient of determination (R²), you can use the formula R² = SSR/SSt. Therefore, R² = 1,750 / 1,809. After calculating, you get an approximate R² value rounded to three decimal places.

R² value provides an insight into the amount of variability in the dependent variable (y) that can be explained by the independent variables (x₁, x₂, x₃, and x₄) in the regression model.