Question

Ten observations were provided for a dependent variable y and two independent variables x₁ and x₂; for these data, SST =15,187.1 and SSR =14,063.5. (a) Compute R²

Answer 1

R² represents the proportion of variation in the dependent variable explained by the independent variables.

Step-by-step explanation:

R², or the coefficient of determination, represents the proportion of variation in the dependent variable y that can be explained by the independent variables x₁ and x₂. To compute R², you need the values of SSR (sum of squared regression) and SST (total sum of squares). R² can be calculated as SSR divided by SST.

1. Given SSR = 14,063.5 and SST = 15,187.1
2. R² = SSR/SST
3. Substituting the values, R² = 14,063.5/15,187.1
4. R² ≈ 0.9263 (rounded to four decimal places)

Therefore, R² is approximately 0.9263, indicating that about 92.63% of the variation in the dependent variable y can be explained by the independent variables x₁ and x₂.