The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1

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The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1

) and their gender (x2) (0 if male and 1 if female).
ŷ = 30 + 0.7x1 + 3x2

Also provided are SST = 1200 and SSE = 384.
The multiple coefficient of determination is _____.

a. .50
b. .42
c. .68
d. .32

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-04-11T06:33:17+03:00

Thus, the most suitable answer is b..42.Step-by-step reasoning:Prior concepts include an explanation of Analysis of variance (ANOVA), which is employed to assess variances among group averages within a sample. The sum of squares constitutes the total squared variation where variation is defined as the disparity between each value and the grand mean. The correlation coefficient evaluates the strength of the correlation between two variable movements, noted as r, with values bounded between -1 and 1. In conducting multiple regression analysis, we seek to ascertain the relationship among multiple independent (predictor) variables and a dependent (criterion) variable.Solution:Assuming the presence of $k$ independent variables and $j=1,\dots,j$ individuals, we can articulate various formulas of variation: We also possess a characteristic identified as $SST=SS_{regression}+SS_{error}$ . The model's degrees of freedom in this circumstance is represented by $df_{model}=df_{regression}=k=2$ , with k =2 indicative of the variable count. The error's degrees of freedom is articulated by $df_{error}=N-k-1=30-2-1=27$ . The coefficient of determination in multiple regression is illustrated as: thus, the answer is b..42.