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