Correlation Coefficient Worksheets Grade 11

1. Mason, a hydrologist, is studying the relationship between the depth of a river (in meters) at a specific point and the water flow velocity (in meters per second) at that same point. He collects data from 12 different river locations and computes the following summary statistics: the mean depth is 2.7 meters, the mean velocity is 1.2 meters per second, the standard deviation of depth is 0.7 meters, the standard deviation of velocity is 0.4 meters per second, and the sum of the products of the z-scores (Σzₓzᵧ) is 7.7. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between river depth and water flow velocity.
2. A scatter plot shows the relationship between the number of hours per week Aroha spends on creative writing (x) and her score on a vocabulary test (y) for 7 weeks. The data points are: (3, 51), (5, 59), (7, 67), (9, 75), (11, 83), (13, 91), (15, 99). Calculate the Pearson correlation coefficient r for this data, and interpret its strength and direction.
3. Isabella, a marine biologist, is studying the relationship between the surface water temperature (in degrees Celsius) and the number of sea stars observed per square meter on a rocky shore. She collects data from 12 different tide pools and records the following summary statistics: the mean temperature is 17°C, the mean sea star count is 22 per m², the standard deviation of temperature is 3°C, the standard deviation of sea star count is 7 per m², and the sum of the products of the z-scores (Σzₓzᵧ) is 8.8. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between surface water temperature and sea star abundance.

…and 2 more problems

1. A scatter plot shows the relationship between the number of hours students spend practicing piano each week (x) and their performance scores on a standardized music assessment (y) for 25 students. The data points form a linear pattern with a correlation coefficient of r = -0.72. The regression equation is ŷ = -2.8x + 92. If a student practices for 6 hours per week, what performance score would you predict using the least squares regression line?
2. Noah, a sports scientist, is studying the relationship between the number of hours of strength training per week (x) and the maximum bench press weight in kilograms (y) for 11 athletes. He collects the following summary statistics: the mean of x is 6 hours, the mean of y is 81 kg, the standard deviation of x is 2 hours, the standard deviation of y is 11 kg, and the sum of the products of z-scores (Σzₓzᵧ) is 8.6. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between weekly strength training hours and maximum bench press weight.
3. Given the dataset: (2, 5), (4, 11), (6, 17), (8, 23), compute the Pearson correlation coefficient r = ?

…and 3 more problems

1. Matiu recorded the number of hours he spent on creative writing per week (x) and the number of pages he wrote (y) over 6 weeks. The data are shown in the scatter plot: (12, 18), (14, 22), (16, 26), (18, 30), (20, 34), (22, 38). Calculate the Pearson correlation coefficient r for this data, and interpret its strength and direction.
2. A research team is studying the relationship between study time and exam scores. They collect data from 15 students and calculate the correlation coefficient as r = 0.72. The team wants to test if this correlation is statistically significant at α = 0.05. Using the critical value table for correlation coefficients with 13 degrees of freedom, the critical value is 0.514. Should the researchers reject the null hypothesis that there is no correlation between study time and exam scores?
3. A scatter plot shows the relationship between the number of hours Noah spends on self-study per week (x) and his score on a physics quiz (y) over 6 weeks. The data points are: (1, 31), (2, 36), (4, 46), (5, 51), (7, 61), (8, 66). Calculate the Pearson correlation coefficient r to three decimal places, and interpret its strength and direction.

…and 2 more problems