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

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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