Math Problem Statement
Here are two sets of bivariate data with the same response variable. The first contains the variables x & y. The second contains the variables w & y
xy
65.6
78.3
64
57.2
68
72.2
70.4
80.2
64.4
84.4
60.2
59.7
58
67.8
57.2
61.9
wy
86.6
64.6
80
53
102.8
105.7
71.9
48.7
79.9
58.9
75.7
48.9
84.9
96.3
80.7
59.4
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x: 65.6,64,68,70.4,64.4,60.2,58,57.2
y: 78.3,57.2,72.2,80.2,84.4,59.7,67.8,61.9
w: 86.6,80,102.8,71.9,79.9,75.7,84.9,80.7
y: 64.6,53,105.7,48.7,58.9,48.9,96.3,59.4
The correlation between the first variable () and the response variable () is . (Show 3 decimals)
The correlation between the second variable () and the response variable () is . (Show 3 decimals)
Which explanatory variable has a stronger relationship with the response variable (y)?
The first variable (x) has a stronger relationship with the response variable (y).
The second variable (w) has a stronger relationship with the response variable (y).
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation Coefficient
Bivariate Data
Formulas
Pearson correlation coefficient formula: r = Σ((X - X̄)(Y - Ȳ)) / sqrt(Σ(X - X̄)² * Σ(Y - Ȳ)²)
Theorems
Pearson's Correlation Theorem
Suitable Grade Level
Grades 10-12