Lab #4: Correlation and Linear Regression (11.25 points) Work on this lab by yourself or in a group of up to 3 people. This lab is due at the beginning of the next class. Please turn in a hard copy or upload a word/pdf document to the Lab #4 Assignment Submission Folder in D2L. Please do not turn in a photo of this document. The observed data for ten participants is as follows within the "data matrix": Subject Push-Ups Sit-Ups (X) (Y) A 20 10 B 18 30 C 16 30 D 15 40 E 15 20 F 14 25 G 14 H 20 13 20 10 15 You might want to calculate the following values in advance because you will need them later (no points - but for your convenience). M. = M, = EX = EY = EX? = IY' = EXY =Perform each of the calculations and/or answer each of the questions as indicated. Please use 2 decimals when needed from this point forward. I) Calculate the standard deviation for each variable (2.5 points - 1.25 point for each variable). Start with the two equations provided below and show your work. Ex - (Ex) Sy n n - 1 7 - 12) Use the information for subject B, and calculate the z-scores for both Push-ups and Sit-Ups (2.5 points - 1.25 point for each variable). Start with the two equations provided below and show your work. _X - My note that My is the same as X Y - My note that M, is the same as Y SY3) Calculate the correlation coefficient between variables X and Y (2.5 points - 1.25 point for numerator and denominator). Start with the equation provided below and show your work. "(EXY) -(EX) (EY)4) Calculate the regression line equation (2.5 points - 1.25 point for each coefficient). Start with the two equations provided below and show your work. b= " (EXY ) - (EX) (EY) c = Y-bX "(EX) -(Er)5) Insert by hand an approximation of the "line of best fit" on the scatterplot below. (1.25 points - .75 for b and .50 for c) 40.00- O 35.00- 30.00- O O SIT UPS 25.00- O 20.00- ooo 15.00- O 10.00- O O 00 5.00 10.00 15.00 20.00 PUSH_UPS