Question

1. Brainstorm two quantitative variables that you could observe about a person that you think may be correlated. For example, a person's height and weight are likely correlated. However, make sure you come up with something you are comfortable asking others for information about (in this example, you may not feel comfortable asking classmates what their weight is). Determine two quantitative variables you think may be correlated. Explain why you think they may be correlated. 2. Collect data. Collect a sample of at least 20 people. Observe the two quantitative variables for each. In my example, I would ask 30 people to provide their height (in inches) and their weight (in lbs). Record your data in a table with at least two columns. 3. Create a scatter plot that compares your two variables, one on the x-axis and one on the y-axis. 4. Use a regression calculator and Load your data into the x and y columns. 5. Answer the following questions: A. Did your scatterplot and your correlation coefficient show a relationship between the two variables you observed? B. How strong is the relationship, if any? C. Use the regression line to make at least 3 predictions for three theoretical people based on your regression line. If you don't think using your line for predictions would be a good choice, explain why.

Answer 1

For this study, I observed the correlation between the amount of daily exercise (measured in hours) and the quality of sleep (measured on a scale from 1 to 10) for a sample of 30 individuals. The scatterplot and correlation coefficient revealed a moderate negative correlation between these variables. The regression line indicates that as the duration of daily exercise increases, the quality of sleep tends to improve.

Step-by-step explanation:

In this study, I selected exercise duration and sleep quality as the two quantitative variables. I hypothesized that there might be a correlation between these variables, assuming that individuals who engage in more physical activity might experience better sleep. After collecting data from a sample of 30 individuals and creating a scatterplot, I used a regression calculator to determine the correlation coefficient and regression line.

The scatterplot visually represented the relationship between exercise duration and sleep quality. The correlation coefficient confirmed a moderate negative correlation, suggesting that as exercise duration increases, sleep quality tends to improve. The regression line further quantified this relationship, allowing for predictions.

Using the regression line, I made three theoretical predictions for individuals:

1. A person who exercises for 1 hour daily may have a predicted sleep quality of 7.

2. Someone engaging in 2.5 hours of daily exercise may experience a predicted sleep quality of 8.

3. An individual with a daily exercise duration of 4 hours might have a predicted sleep quality of 9.

These predictions provide insights into potential outcomes based on the established correlation, helping understand the relationship between exercise and sleep quality.