Asked by Mallory Sheets on Jun 03, 2024
Verified
In a multiple regression analysis involving 40 observations and 5 independent variables,the following statistics are given: Total variation in y = 350 and SSE = 50.Then,the coefficient of determination is:
A) 0.8408
B) 0.8571
C) 0.8469
D) 0.8529
Coefficient of Determination
A statistical measure, often denoted as R^2, that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
Independent Variables
Variables in an experiment or model that are manipulated or changed to observe their effect on dependent variables.
Total Variation
The overall measure of the spread or dispersion of a set of data points.
- Familiarize with the role and relevance of the coefficient of determination in the context of multiple regression.
Verified Answer
R-squared = 1 - (SSE / SST)
where SSE is the sum of squared errors and SST is the total sum of squares.
In this case, we are given that SST = 350 and SSE = 50. Therefore,
R-squared = 1 - (50 / 350) = 0.8571
So the best choice is B.
Learning Objectives
- Familiarize with the role and relevance of the coefficient of determination in the context of multiple regression.
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