Math Problem Statement

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Calculate the correlation​ coefficient, r. Start 2 By 10 Table 1st Row 1st Column Temperatur comma x 2nd Column 76 3rd Column 89 4st Column 95 5st Column 94 6st Column 92 7st Column 102 8st Column 79 9st Column 104 10st Column 84 2nd Row 1st Column Number of absences comma y 2nd Column 12 3rd Column 16 4st Column 19 5st Column 19 6st Column 17 7st Column 24 8st Column 13 9st Column 24 10st Column 14 EndTable

Question content area bottom Part 1 A. 0.890 B. 0.980 C. 0.819 D. 0.881

Solution

numpy as np

Given data

temperature = np.array([76, 89, 95, 94, 92, 102, 79, 104, 84]) absences = np.array([12, 16, 19, 19, 17, 24, 13, 24, 14])

Calculate the correlation coefficient

correlation_coefficient = np.corrcoef(temperature, absences)[0, 1] correlation_coefficientThe correlation coefficient, rr, is approximately 0.9800.980. Therefore, the correct answer is:

B. 0.980

Would you like details about the calculation process or the interpretation of this result?

Here are five follow-up questions:

  1. How is the correlation coefficient interpreted in the context of this data?
  2. What does a positive correlation coefficient signify in this case?
  3. Can a high correlation coefficient imply causation between temperature and absences?
  4. How could this analysis be visualized using a scatter plot?
  5. What might be the limitations of using correlation in this scenario?

Tip: Always ensure that data is properly scaled and checked for outliers to avoid skewed correlation results.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient

Formulas

Correlation Coefficient formula: r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)^2 * Σ(y - ȳ)^2)

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

Grades 10-12