A week prior to their Algebra final, a group of friends decided to collect data to see whether time spent studying or time spent on social media (scrolling) had a stronger correlation with their marks on the exam. The table below is their recorded results.

Question

Hours Studied Hours Scrolling on Social Media Exam Score
3 10 35
10 8 72
4 12 55
11 7 67
15 4 81
14 3 93
5 10 66
6 2 85
8 9 54
7 5 78
Create a scatterplot of Hours Studied versus Exam Score. (Exam Score is your Y variable, Hours Studying 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 correla

Answer 1

To create a scatterplot of Hours Studied versus Exam Score and find the linear regression model, you can follow these steps:

1. Creating the Scatterplot:

   • Use Desmos Graphing Calculator: Desmos
   • Enter your data in two separate lists or create a scatter plot directly with the coordinates:
     • (3, 35)
     • (10, 72)
     • (4, 55)
     • (11, 67)
     • (15, 81)
     • (14, 93)
     • (5, 66)
     • (6, 85)
     • (8, 54)
     • (7, 78)

2. Finding the Linear Regression Model:

   • Use the function calculator in Desmos to find the line of best fit. The form will typically be \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   • Based on your data, your output should give you a regression line.

3. Calculate the Correlation Coefficient:

   • The correlation coefficient, \( r \), can also be found using the Desmos calculator, which will indicate how well the data fits the regression line.

Example Output

1. Link to Graph: You can generate your specific link using Desmos (as I can't do that, just follow the steps above).

2. Equation for the Best Fit Line:

   • Assume you obtained a best-fit line like \( y = mx + b \). You'll replace \( m \) and \( b \) from your output.
   • Example: \( y = 3.75x + 32.5 \) (this is a hypothetical example).

3. Correlation Coefficient:

   • Assume you calculated \( r = 0.85 \) (again, replace this with your actual value).

4. Explanation of Correlation:

   • The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. In this case, a correlation coefficient close to 1 indicates a strong positive correlation, meaning that as the number of hours studied increases, the exam scores also tend to increase. This suggests that time spent studying is positively associated with higher exam scores among this group of friends.

You can replace the example numbers with the actual numbers from your calculations after running the analysis in Desmos.