6.3 The Least-Squares Regression Line Learning Goal: For a linear relationship, use the least squares regression line to summarize the overall pattern and to make predictions. Learning Objective: Calculate prediction errors (residuals) and understand the idea of minimizing the sum of the squared errors (SSE). 1) Here is data from 1254 New York public schools. There is a strong linear relationship between students' English proficiency and their math proficiency (r = 0.94). Math proficiency 3.5 2.5 English proficiency 2.5 3 3.5 a) Which line do you think is a better summary of the linear pattern in the data? Why? b) Here are the equations of these lines: A: predicted math proficiency = 1.17.(English proficiency) - 0.23 B: predicted math proficiency = 1.17.(English proficiency) + 0.10 Predict the math proficiency at a school with an average English proficiency score of 3 using both lines. Which do you think is a more reliable prediction? Why