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
The correlation between the first variable (x) and the response variable (y) is 0.602.
The correlation between the second variable (w) and the response variable (y) is 0.864.
Thus, the second variable (w) has a stronger relationship with the response variable (y) because its correlation is higher.
Do you want more details or have any questions?
Here are 5 related questions to deepen your understanding:
- How does Pearson correlation coefficient measure linear relationships?
- What happens if the correlation between two variables is negative?
- Can correlation imply causation in any case?
- How would you interpret a correlation of 0?
- What other types of correlation exist besides Pearson's?
Tip: Correlation values close to 1 or -1 indicate a strong relationship, while values near 0 show a weak relationship.
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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