The data below are the average one-way commute times (in minutes) of selected students during a summer literature class and the number of absences for those students for the term. Calculate the linear correlation coefficient.
Selected students means you are dealing with a sample from a population.
The best you can do with a sample is to estimate the correlation coefficient of the population, or the correlation coefficient of the sample.
See the formulas and examples from:
http://stattrek.com/statistics/correlation.aspx
http://www.vitutor.com/statistics/regression/correlation_coefficient.html
To calculate the linear correlation coefficient, also known as the Pearson correlation coefficient, you need to have two sets of data: one for commute times and one for absences. Please provide these two sets of data in order to proceed with the calculation.
To calculate the linear correlation coefficient, you will need to know the average one-way commute times and the number of absences for each student. Let's assume you have a sample of n students.
1. First, organize the data into two columns: one for average one-way commute times and the other for the number of absences for each student.
2. Calculate the mean (average) of the commute times (x̄) and the mean of the absences (ȳ).
3. Calculate the deviations for each data point:
a. For each commute time, subtract the mean of commute times (x - x̄).
b. For each number of absences, subtract the mean of absences (y - ȳ).
4. Calculate the squared deviations for each data point:
a. Square each deviation obtained in step 3. (x - x̄)^2 and (y - ȳ)^2.
5. Calculate the product of deviations for each data point:
Multiply the deviation of the commute time by the deviation of the number of absences for each student. (x - x̄) * (y - ȳ)
6. Calculate the sum of the squared deviations for commute times (Σ(x - x̄)^2), the sum of the squared deviations for absences (Σ(y - ȳ)^2), and the sum of the product of deviations (Σ(x - x̄) * (y - ȳ)).
7. Calculate the correlation coefficient (r) using the following formula:
r = Σ(x - x̄) * (y - ȳ) / sqrt[Σ(x - x̄)^2 * Σ(y - ȳ)^2]
8. After applying the formula, you will get the correlation coefficient (r) as the result. The value of r will range from -1 to +1, where -1 indicates a strong negative correlation, +1 indicates a strong positive correlation, and 0 indicates no correlation.
Note: Alternatively, you can use spreadsheet software or statistical software to calculate the correlation coefficient, which will automate the process for you.
Once you have all the necessary data and follow the steps correctly, you will be able to calculate the linear correlation coefficient for the given data.