Based on the scatter plot provided, I can help guide you through solving this problem. Here’s how we can proceed:

1. Find the Line of Best Fit (Part a):

   • We approximate a line of best fit for the scatter plot. This line typically has the form: $\hat{y} = mx + b$ where $m$ is the slope and $b$ is the y-intercept.
   • By observing the pattern in the data points, estimate the slope $m$ and the y-intercept $b$. You can do this by selecting two points on the line that closely fits the data trend, then use them to calculate the slope.
   • Once you calculate $m$ and $b$, round each to the nearest hundredth.

2. Prediction for 60 Minutes of Studying (Part b):

   • Use the equation from part (a) and plug in $x = 60$ (for 60 minutes of studying) to calculate the predicted quiz score, $\hat{y}$.
   • Again, round this prediction to the nearest hundredth.

Would you like a detailed example on how to select points and calculate the slope and intercept, or do you have specific points you want to use?

Related Questions for Further Practice

1. How do you calculate the slope between two points on a graph?
2. What is the significance of the y-intercept in a real-world context?
3. Why do we round coefficients in regression analysis?
4. How would the equation change if the data had a stronger upward or downward trend?
5. Can you explain how the accuracy of predictions changes with a higher or lower correlation between variables?

Tip: When approximating a line of best fit, choosing points that span the range of the data often results in a more accurate fit.