Assignment 8 - Ryan Kindall

Assignment #8 Chapter 2 Least-Squares Regression pp. 107-123: Homework: #1-3 The regression line: y = b 0 + b 1 x Least-squares regression line : minimizes the differences between all points in the graph and the regression line . y-hat ( ^ y ) is the equation for the regression line and any individual value substituted yields a predicted value ^ y = b 0 + b 1 x b 1 = r s y s x b 0 = y − b 1 ¿ x ¿ Predicted values Slope (b 1 ) Intercept (b 0 ) 1. The scatterplot to the left represents the relationship between avoidant coping and life satisfaction . Based on the values provided below, compute the equation for the least-squares regression line. x = avoidant coping y = life satisfaction r =-.26 s x =.92 s y =.90 x = ¿ 2.72 y = ¿ 4.82 Equation: Now using this equation, what is the predicted Life satisfaction value for the following avoidant coping scores? Avoidant coping: 5 Predicted Life satisfaction: __________ Avoidant coping: 6.5 Predicted Life satisfaction: ____________ Avoidant coping: 1.5 Predicted Life satisfaction: ____________ B1 = -.26 (.9/.92) —> -.26(.978) = -.25 (-.254) B0 = 4.82 - (-.25)(2.72) = 4.82 + .68) = 5.50 ŷ = 5.5 + .25x ŷ = 5.5 + -.25(5) ŷ = 5.5 + (-1.25) ŷ = 4.25 4.25 ŷ = 5.5 + -.25(6.5) ŷ = 5.5 + (-1.625) ŷ = 3.875 —> 3.88 3.88 ŷ = 5.5 + -.25(1.5) ŷ = 5.5 + (-0.375) ŷ = 5.125 —> 5.13 5.13

2. The scatterplot to the left represents the relationship between social support and life satisfaction . Based on the values provided below, compute the equation for the least-squares regression line. x = social support y = life satisfaction r = .36 s x =.89 s y =.90 x = ¿ 3.52 y = ¿ 4.82 Equation: Now using this equation, what is the predicted Life satisfaction value for the following social support scores? Social support: 5 Predicted Life satisfaction: __________ Social support: 6.5 Predicted Life satisfaction: ____________ Social support: 1.5 Predicted Life satisfaction: ____________ ^ y = b 0 + b 1 x b 1 = r s y s x b 0 = y − b 1 ¿ x ¿