Questions: Use the following information for numbers 1 - 10: In a recent training, Mrs. Anschicks noticed that the number of people paying attention was declining throughout the day. She collected the following data: Time (hours) 0 1 2 3 4 5 6 # people paying attention 80 68 62 50 48 32 21 1. Make a scatterplot of the data using the applet and sketch it below. 2. Calculate the correlation coefficient, 3. Interpret (Use DOFS to describe). 4. Identify the least squares regression line (LSRL): 5. Use your LSRL to make a prediction for the number of people paying attention at 2.5 hours.

Use the following information for numbers 1 - 10: In a recent training, Mrs. Anschicks noticed that the number of people paying attention was declining throughout the day. She collected the following data: Time (hours) 0 1 2 3 4 5 6 # people paying attention 80 68 62 50 48 32 21 1. Make a scatterplot of the data using the applet and sketch it below. 2. Calculate the correlation coefficient, 3. Interpret (Use DOFS to describe). 4. Identify the least squares regression line (LSRL): 5. Use your LSRL to make a prediction for the number of people paying attention at 2.5 hours.
Transcript text: Use the following information for numbers 1 - 10: In a recent training, Mrs. Anschicks noticed that the number of people paying attention was declining throughout the day. She collected the following data: \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Time (hours) & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \# people paying attention & 80 & 68 & 62 & 50 & 48 & 32 & 21 \\ \hline \end{tabular} 1. Make a scatterplot of the data using the applet and sketch it below. 2. Calculate the correlation coefficient, 3. Interpret (Use DOFS to describe). 4. Identify the least squares regression line (LSRL): 5. Use your LSRL to make a prediction for the number of people paying attention at 2.5 hours.
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Solution

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Solution Steps

Step 1: Scatterplot of the data

The data points are:

  • Time (hours): [0, 1, 2, 3, 4, 5, 6]
  • Number of people paying attention: [80, 68, 62, 50, 48, 32, 21]
Step 2: Calculate the correlation coefficient

The correlation coefficient \( r \) is calculated using the formula: \[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \] where \( n \) is the number of data points.

Step 3: Interpret (Use DOFS to describe)
  • Direction: The correlation is negative, indicating that as time increases, the number of people paying attention decreases.
  • Outliers: There do not appear to be any significant outliers.
  • Form: The relationship appears to be linear.
  • Strength: The correlation coefficient indicates a strong relationship.

Final Answer

  1. Scatterplot of the data:
  2. The correlation coefficient is approximately \( r = -0.9734 \).
  3. The relationship is strong, negative, linear, and there are no significant outliers.

{"axisType": 3, "coordSystem": {"xmin": -1, "xmax": 7, "ymin": 0, "ymax": 90}, "commands": ["y = 80", "y = 68", "y = 62", "y = 50", "y = 48", "y = 32", "y = 21"], "latex_expressions": ["$y = 80$", "$y = 68$", "$y = 62$", "$y = 50$", "$y = 48$", "$y = 32$", "$y = 21$"]}

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