Based on the correlation coefficient for the data, what type of linear association exists between hours worked and overall grade average?

Steps to Solve

1. Understand the Data Relationship
   The data presented shows two variables: "Hours Worked" (independent variable) and "Overall Grade Average" (dependent variable). To determine the type of linear association, we will examine the trend in the data.

2. Identify the Direction of the Association
   Look for a trend based on the provided values. Generally, if increasing values in one variable (hours worked) correspond with increasing values in the other variable (grade average), it indicates a positive relationship. Conversely, if increasing hours lead to decreasing grades, it indicates a negative relationship.

3. Visualize the Data
   To better understand the correlation, it can be helpful to create a scatter plot (though not required here). Plotting the hours on the x-axis and grades on the y-axis would help to visualize the relationship.

4. Calculate the Correlation Coefficient
   Although we will not compute it realistically, knowing that a correlation coefficient close to 1 indicates a strong positive relationship, and one close to -1 indicates a strong negative relationship can guide our decision. Values near 0 suggest weak relationships.

5. Evaluate the Pattern from the Data
   Looking at the table data:

   • 15 hours, Grade 86
   • 30 hours, Grade 72
   • 27 hours, Grade 77
   • 25 hours, Grade 83
   • 16 hours, Grade 87
   • 20 hours, Grade 90
   • 12 hours, Grade 94

   As the hours worked increases, the overall grade average does not consistently increase or decrease, suggesting a more complicated relationship.

6. Determine the Type of Association
   Given the varying grades for increasing hours and without significant upward or downward trends, we lean towards a weak positive association due to some increase towards the end but erratic overall.