Math Problem Statement
Solution
To find the correlation coefficient , we need to calculate it using the formula:
[ r = \frac{n\sum(xy) - \sum x \sum y}{\sqrt{\left[n\sum(x^2) - (\sum x)^2\right] \left[n\sum(y^2) - (\sum y)^2\right]}} ]
Where:
- is the number of weeks
- is the gain in reading speed
- is the number of data points
I will calculate step by step.
Table summary:
The given data points are:
\hline \text{No. of Weeks} (x) & \text{Gain in Reading Speed} (y) \\ \hline 20 & 18 \\ 26 & 13 \\ 30 & 39 \\ 16 & 51 \\ 9 & 18 \\ \hline \end{array}$$ I will now calculate the necessary sums. numpy as np # Data x = np.array([20, 26, 30, 16, 9]) # No. of weeks y = np.array([18, 13, 39, 51, 18]) # Gain in reading speed # Number of data points n = len(x) # Calculations for the correlation coefficient sum_x = np.sum(x) sum_y = np.sum(y) sum_xy = np.sum(x * y) sum_x2 = np.sum(x**2) sum_y2 = np.sum(y**2) # Correlation coefficient formula numerator = n * sum_xy - sum_x * sum_y denominator = np.sqrt((n * sum_x2 - sum_x**2) * (n * sum_y2 - sum_y**2)) r = numerator / denominator # Result rThe correlation coefficient $$r$$ is approximately $$0.0705$$ (rounded to 4 decimal places). This indicates a very weak positive relationship between the number of weeks and the gain in reading speed. Would you like me to explain any step in detail or perform further analysis? --- Here are 5 related questions to expand understanding: 1. What does the value of $$r$$ imply about the relationship between two variables? 2. How can the correlation coefficient $$r$$ be tested for statistical significance? 3. Can $$r$$ identify non-linear relationships between variables? 4. What would happen to $$r$$ if the data contained outliers? 5. How is $$r^2$$ (the coefficient of determination) interpreted in this context? **Tip:** When calculating $$r$$, always double-check data entry and computations for accuracy, as small errors can greatly affect the result.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Data Analysis
Formulas
Correlation coefficient formula: r = (nΣ(xy) - ΣxΣy) / sqrt([nΣ(x²) - (Σx)²][nΣ(y²) - (Σy)²])
Theorems
Linear Correlation
Suitable Grade Level
Grades 10-12
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