Vitruvian Man Name: Maddon Hob Choi Part II - Height vs Hand Span Gather data! Gather data for the class one last time. Use the height you already measured and then measure your hand span. Fill in the table with the class data and plot those ordered pairs X = Height y = _ Handspan Height Hand Span Height 178 Hand Span Height Hand Span 765 176 4 163 165 16 20 185 17.5 12 16 167. 5 61 18.5 N/ 160 12:5 172 V 18 178 20 189 179 6 18 179 19 185 Lq 185 20 174 20 19.5+ 19 18.5 18 Handspan 175 17 16- 5- 1 16 160 165 119 15 180 180 185% 190 X Height1) What is the DIRECTION of this graph? Explain why this makes sense. It's a uphill direction, reflecting a positive correlation. There is a positive correlation between height and hand span. 2) Vitruvius predicted that the height of a man is equal to one tenth the length of his hand span. Write 5 ordered pairs that would show this relationship: x = height y = hand span 165 179.5 18 179 189 165 16 3) What is the equation of the line you drew? (Remember: y = mx + b ; m = slope, and b = y-intercept) 18-116 - 2 =14 Y= 14x+b 16=19 (165)+6 17:4.5-165 14.5 1 16 = 23.1+ 6 y = . 14 x - 7.1 - 7.1 =6 4) Using your calculator, find the Least Squares Regression Line: *=. 09 x + 3. 32 5) Compare Vitruvius's line with the least squares regression line from your calculator. Are they the same or different? Why? Both lines are Similiar, in that their slope is less than one, but their y-intercept is very different. The slope doesn't change, much with new mumbers, but the y-interest can be effected drastically with new y-intercepts. 6) If a student had a height of 180cm, what is their hand span predicted to be? Use your LSRL from your calculator. yExt 3.32 1= 09 ( 180)+ 3.32 4= 19,527 (19.52 units 7) What is the meaning of the slope in this context? For ever I unit of increased height, there is a . od increase in handspan units.8) Calculate the Least Squares Regression Line by hand. sy = 1. 16 sx = 9.3 *= 174.48 ,= 18:26 L2 L3 L4 L5 Put all your x- Put all your y- Formula: Formula: Formula: values in this values in this L1 - x L2 - y = 13 * L4 list list Sx Sy Sum of list 5 = n = total number of students = r = - n - 1 (sum of list 5) Once we have r, we can use the five numbers to calculate the slope and y-intercept of our least squares regression line. Sy = SX = x = r= y = ax +b a =r b = y - ax