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USE THE TABLE ABOVE

Create a scatterplot of Hours Scrolling On Social Media versus Exam Score. (Exam Score is your Y variable, Hours Scrolling Social Media is your X variable) Use the technology tools to create the linear regression model for the scatterplot to put the required answers in the box below.

In the answer box below provide:

Link to your graph (USE DESMOS)
The equation for your best fit line
The correlation coefficient for your data
An explanation as to what correlation you see via the graph and what it means in context.
(5 points)

1 answer

I'm unable to create visual content or directly interact with web tools like Desmos. However, I can guide you through how to create the scatterplot and analyze the data.

  1. Creating a Scatterplot in Desmos:

    • Go to Desmos Graphing Calculator.
    • Enter your data in two lists:
      • For example, if your data points for "Hours Scrolling on Social Media" (X values) are [1, 2, 3, 4, 5] and for "Exam Scores" (Y values) are [95, 90, 85, 70, 60], you can input: 
        A = [1, 2, 3, 4, 5]
B = [95, 90, 85, 70, 60]
    • Then plot the points using: 
      (A, B)
    • To perform linear regression, type in the linear regression function, which will look like: 
      y1 ~ mx1 + b

  2. Obtaining the Linear Regression Model:

    • After entering your data, Desmos will provide you with the best fit line in the format \( y = mx + b \).
    • Note the values for \( m \) (slope) and \( b \) (y-intercept) from the results.

  3. Finding the Correlation Coefficient:

    • Desmos will also calculate the correlation coefficient \( r \) for you. This value will range from -1 to 1, indicating the strength and direction of the linear relationship (where 1 is a perfect positive correlation, -1 is a perfect negative correlation, and 0 indicates no linear correlation).

  4. Interpretation:

    • If you observe a downward trend in your scatterplot (a negative slope), and your correlation coefficient is close to -1, this indicates that as the hours spent scrolling on social media increases, the exam scores tend to decrease. This suggests a negative correlation where excessive social media use may be negatively affecting exam performance.

  5. What to provide in the answer box:

    • The link to your graph on Desmos.
    • The equation of the best fit line (e.g., \( y = -5x + 100 \)).
    • The correlation coefficient (e.g., \( r = -0.95 \)).
    • Your explanation of correlation, as outlined above.

If you have specific data, I can help further refine these steps based on your actual data points!