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, , is approximately . 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:
- How is the correlation coefficient interpreted in the context of this data?
- What does a positive correlation coefficient signify in this case?
- Can a high correlation coefficient imply causation between temperature and absences?
- How could this analysis be visualized using a scatter plot?
- 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.
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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
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