Question

In a simple linear regression based on 30 observations, it is found that SSE- 2,540 and SST- 13,870 a. Calculate and se (Round your answers to 2 decimal places.) 5 b. Calculate the coefficient of determinationR. (Round your answer to 4 decimal places.) Coefficient of Determination

Answer 1

The coefficient of determination (R²) is calculated to be approximately 0.8170, implying that roughly 81.70% of the variation in the dependent variable is explained by the model. The standard error of estimate (se) is approximately 9.49.

Step-by-step explanation:

The subject question is related to simple linear regression, a statistical method used to model the relationship between a dependent variable and one independent variable. The formula for calculating the coefficient of determination, represented by R², is derived from the values of the Sum of Squares due to Error (SSE) and the Total Sum of Squares (SST). The coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable.

To calculate R², use the formula R² = 1 - (SSE/SST). Substituting the given values yields R² = 1 - (2540/13870), which equals approximately 0.8170 when rounded to four decimal places. This means about 81.70% of the variation in the dependent variable can be explained by the independent variable in the regression model.

The standard error of estimate, or se, can be calculated using the formula se = √(SSE/(n-2)), where n is the number of observations. Substituting the given values yields se = √(2540/28), which equals approximately 9.49 when rounded to two decimal places.

Answer 2

The standard error of the estimate (se) is approximately 9.50, and the coefficient of determination (R^2) is 0.8168, meaning that 81.68% of the variance in the dependent variable is explained by the regression model.

Step-by-step explanation:

The student has asked to calculate the standard error of the estimate (se) and the coefficient of determination (R) for a simple linear regression based on 30 observations with given SSE (Sum of Squares due to Error) and SST (Total Sum of Squares).

To calculate the standard error of the estimate:

se = √(SSE / (n-2))

se = √(2540 / (30-2))

se = √(2540 / 28)

se ≈ 9.50 (rounded to two decimal places).

To calculate the coefficient of determination (R²):

R² = 1 - (SSE / SST)

R² = 1 - (2540 / 13870)

R² = 1 - 0.1832

R² = 0.8168 (rounded to four decimal places).

The coefficient of determination, R², indicates the proportion of the variance in the dependent variable that is predictable from the independent variable in the regression model. In this case, 81.68% of the variance can be explained by the model.