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
23.3
71.9
47.2
92.7
6.1
44.3
58.3
134.6
40.7
145.5
34.7
25.4
20.8
10.8
48.8
119.7
wy
16.1
51.3
44.6
14.1
23.4
39.5
26.7
29.2
41.7
10.1
7.8
58.4
44.5
10
38.3
13.6
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x: 23.3,47.2,6.1,58.3,40.7,34.7,20.8,48.8
y: 71.9,92.7,44.3,134.6,145.5,25.4,10.8,119.7
w: 16.1,44.6,23.4,26.7,41.7,7.8,44.5,38.3
y: 51.3,14.1,39.5,29.2,10.1,58.4,10,13.6
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 .
The correlation between the second variable (w) and the response variable (y) is .
Thus, the second variable (w) has a stronger relationship with the response variable (y), as the magnitude of its correlation is greater.
Would you like a deeper explanation on correlations or how they are interpreted?
Here are 5 related questions:
- What does a positive or negative correlation imply?
- How does correlation affect regression analysis?
- What are the limitations of using correlation alone to interpret relationships?
- Can two variables have a strong correlation without one causing the other?
- How would we test if these correlations are statistically significant?
Tip: Always check the sign of the correlation. A negative correlation indicates an inverse relationship!
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Bivariate Data
Formulas
Pearson correlation coefficient formula: r = Σ[(xi - mean(x))(yi - mean(y))] / sqrt(Σ(xi - mean(x))^2 * Σ(yi - mean(y))^2)
Theorems
Correlation Theorem: A correlation close to 1 or -1 indicates a strong linear relationship, while a correlation near 0 suggests weak or no linear relationship.
Suitable Grade Level
Grades 10-12
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