pub fn correlation(x: &[f64], y: &[f64]) -> StatsResult<f64>Expand description
Calculate Pearson correlation coefficient between two datasets
Examples found in repository?
examples/basic_usage.rs (line 34)
3fn main() {
4 println!("=== Statify Statistics Library Demo ===\n");
5
6 // Basic descriptive statistics
7 let data = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
8
9 println!("Dataset: {:?}\n", data);
10 println!("Descriptive Statistics:");
11 println!(" Mean: {:.2}", data.mean().unwrap());
12 println!(" Median: {:.2}", data.median().unwrap());
13 println!(" Std Dev: {:.2}", data.std_dev().unwrap());
14 println!(" Variance: {:.2}", data.variance().unwrap());
15 println!(" Min: {:.2}", data.min().unwrap());
16 println!(" Max: {:.2}", data.max().unwrap());
17 println!(" Range: {:.2}", data.range().unwrap());
18 println!(" Sum: {:.2}", data.sum().unwrap());
19
20 // Percentiles and quartiles
21 println!("\nPercentiles:");
22 println!(" 25th percentile (Q1): {:.2}", data.quartile_1().unwrap());
23 println!(" 50th percentile (Median): {:.2}", data.percentile(50.0).unwrap());
24 println!(" 75th percentile (Q3): {:.2}", data.quartile_3().unwrap());
25 println!(" IQR: {:.2}", data.iqr().unwrap());
26
27 // Correlation and covariance
28 let x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
29 let y = vec![2.0, 4.0, 6.0, 8.0, 10.0];
30
31 println!("\nCorrelation Analysis:");
32 println!(" X: {:?}", x);
33 println!(" Y: {:?}", y);
34 println!(" Correlation: {:.4}", correlation(&x, &y).unwrap());
35 println!(" Covariance: {:.4}", covariance(&x, &y).unwrap());
36
37 // Z-scores
38 let sample = vec![10.0, 20.0, 30.0, 40.0, 50.0];
39 let z_vals = z_scores(&sample).unwrap();
40
41 println!("\nZ-Scores:");
42 println!(" Data: {:?}", sample);
43 println!(" Z-scores: {:?}", z_vals.iter().map(|&x| format!("{:.2}", x)).collect::<Vec<_>>());
44
45 // Real-world example: test scores
46 let test_scores = vec![
47 85.0, 92.0, 78.0, 95.0, 88.0, 76.0, 89.0, 94.0, 81.0, 87.0,
48 ];
49
50 println!("\n=== Real-World Example: Test Scores ===");
51 println!("Scores: {:?}", test_scores);
52 println!(" Average Score: {:.2}", test_scores.mean().unwrap());
53 println!(" Median Score: {:.2}", test_scores.median().unwrap());
54 println!(" Std Deviation: {:.2}", test_scores.std_dev().unwrap());
55 println!(" Lowest Score: {:.2}", test_scores.min().unwrap());
56 println!(" Highest Score: {:.2}", test_scores.max().unwrap());
57 println!(" Score Range: {:.2}", test_scores.range().unwrap());
58}More examples
examples/advanced_statistics.rs (line 54)
6fn main() {
7 println!("=== Advanced Statistics Demo ===\n");
8
9 // Sample dataset: student test scores
10 let scores = vec![
11 85.0, 92.0, 78.0, 95.0, 88.0, 76.0, 89.0, 94.0, 81.0, 87.0, 90.0, 83.0, 86.0, 91.0, 79.0,
12 ];
13
14 println!("📊 Student Test Scores: {:?}\n", scores);
15
16 // Basic statistics
17 println!("Basic Statistics:");
18 println!(" Mean: {:.2}", scores.mean().unwrap());
19 println!(" Median: {:.2}", scores.median().unwrap());
20 println!(" Std Dev: {:.2}", scores.std_dev().unwrap());
21 println!(" Coefficient of Variation: {:.2}%", coefficient_of_variation(&scores).unwrap());
22 println!(" Standard Error: {:.2}", standard_error(&scores).unwrap());
23
24 // Distribution shape
25 println!("\n📈 Distribution Shape:");
26 println!(" Skewness: {:.4}", skewness(&scores).unwrap());
27 println!(" Kurtosis: {:.4}", kurtosis(&scores).unwrap());
28
29 // Normalization
30 println!("\n🔄 Normalized Scores (0-1 scale):");
31 let normalized = normalize_min_max(&scores).unwrap();
32 println!(" First 5: {:?}", &normalized[0..5].iter().map(|&x| format!("{:.2}", x)).collect::<Vec<_>>());
33
34 // Grade scaling (60-100 scale)
35 println!("\n📏 Scaled to 60-100:");
36 let scaled = normalize_range(&scores, 60.0, 100.0).unwrap();
37 println!(" First 5: {:?}", &scaled[0..5].iter().map(|&x| format!("{:.2}", x)).collect::<Vec<_>>());
38
39 // Linear regression: study hours vs test scores
40 println!("\n📉 Linear Regression: Study Hours vs Test Scores");
41 let study_hours = vec![2.0, 3.5, 1.5, 5.0, 3.0, 1.0, 3.5, 4.5, 2.5, 3.0, 4.0, 2.0, 3.0, 4.0, 1.5];
42
43 let regression = linear_regression(&study_hours, &scores).unwrap();
44 println!(" Slope: {:.2} (points per hour)", regression.slope);
45 println!(" Intercept: {:.2}", regression.intercept);
46 println!(" R²: {:.4}", regression.r_squared);
47
48 // Predict score for 6 hours of study
49 let predicted_score = regression.predict(6.0);
50 println!(" Predicted score for 6 hours of study: {:.2}", predicted_score);
51
52 // Correlation analysis
53 println!("\n🔗 Correlation Analysis:");
54 let corr = correlation(&study_hours, &scores).unwrap();
55 println!(" Correlation between study hours and scores: {:.4}", corr);
56
57 // Normal distribution analysis
58 println!("\n📊 Normal Distribution Analysis:");
59 let mean = scores.mean().unwrap();
60 let std_dev = scores.std_dev().unwrap();
61
62 println!(" Using mean={:.2}, std_dev={:.2}", mean, std_dev);
63
64 // Probability of scoring exactly 85
65 let pdf_85 = normal_pdf(85.0, mean, std_dev).unwrap();
66 println!(" PDF at score 85: {:.6}", pdf_85);
67
68 // Probability of scoring 85 or less
69 let cdf_85 = normal_cdf(85.0, mean, std_dev).unwrap();
70 println!(" Probability of scoring ≤85: {:.2}%", cdf_85 * 100.0);
71
72 // Probability of scoring 90 or less
73 let cdf_90 = normal_cdf(90.0, mean, std_dev).unwrap();
74 println!(" Probability of scoring ≤90: {:.2}%", cdf_90 * 100.0);
75
76 // Probability of scoring above 90
77 println!(" Probability of scoring >90: {:.2}%", (1.0 - cdf_90) * 100.0);
78
79 // Real-world interpretation
80 println!("\n💡 Insights:");
81 if regression.r_squared > 0.7 {
82 println!(" ✓ Strong correlation between study hours and test scores!");
83 } else if regression.r_squared > 0.4 {
84 println!(" ≈ Moderate correlation between study hours and test scores.");
85 } else {
86 println!(" ✗ Weak correlation between study hours and test scores.");
87 }
88
89 let skew_val = skewness(&scores).unwrap();
90 if skew_val.abs() < 0.5 {
91 println!(" ✓ The score distribution is approximately symmetric.");
92 } else if skew_val > 0.0 {
93 println!(" ⚠ The distribution is right-skewed (more low scores).");
94 } else {
95 println!(" ⚠ The distribution is left-skewed (more high scores).");
96 }
97
98 let cv = coefficient_of_variation(&scores).unwrap();
99 if cv < 10.0 {
100 println!(" ✓ Low variability: scores are consistent.");
101 } else if cv < 20.0 {
102 println!(" ≈ Moderate variability in scores.");
103 } else {
104 println!(" ⚠ High variability: scores are widely spread.");
105 }
106}