APStatistics Unit 3 Examining Relationships Exam: Free Response Directions: Complete the assignment. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. 1. Given the following observations of quantitative variables X and Y: X 0 1 2 3 Y 3 4 6 10 15 0 (a) Make a scatterplot of the data on the axes. Circle the most influential observation. (4 points) (b) Determine the LSRL of Y on X. Draw this line carefully on your scatterplot. (4 points) (c) What is the definition of a regression outlier? (4 points) (d) Which data point is the biggest regression outlier? (4 points) (e) What is the residual at the point identified in part (c)? (4 points) (f) Construct a residual plot for these data. (4 points) (g) Interpret your residual plot, i.e., what does the residual plot tell you? (4 points) 2. Anthropologists must often estimate from human remains how tall the person was when alive. Carla is studying how overall height can be predicted from the length of leg bone in a group of 36 living males. The data show that the bone lengths have mean 45.9 cm and standard deviation 4.2 cm, the overall heights have mean 172.7 cm and standard deviation 8.14 cm, and the correlation between bone length and height is 0.914. (a) What is the slope of the LSRL of height on bone length? (6 points) (b) About what percent of the observed variation in the heights of the men can be explained by the linear regression of height on bone length? (4 points) (c) Based on your answer to (b), how would you describe the goodness of linear fit? (4 points) (d) Determine the equation of the LSRL of height on bone length. (4 points) 3. Consider the following scatterplot: Provide an approximate equation for the regression line that has been drawn on the plot. (6 points)