10) Data for various drivers is displayed below showing the relationship between their age and the furthest distance atwhich they can read a road sign. The table gives the maximum age, a, in years and the distance, d, in feet. Thescatterplot shows the relationship between age and distance.a)Adagedistance(years) (feet)2357027520284554045552455643506542570375Sign Legibility Distance (feet)600500400300T152535 45 55 65Driver Age (years)Draw your line of best fit through the data points.7585b)Pick two points on your regression line. IMPORTANT: These two points should be on your line and not datapoints from the table. Do not use the y intercept as a point, because the x axis does not start at zero. Write bothcoordinates of your points in the blank lines below.c)Use your two points from part b to find an equation for your line of best fit. Use the letters a and d in yourequation. Do not use the letters x and y. If you end up with decimals in your equation, round to the nearest hundredth.d)Use your equation to estimate the distance at which someone can clearly read a road sign when they are32 years old.

Given information: Age (A) Distance(d) 23 570 27 520 28 455 40 455 52 455 64 350 65 425 70 375 A) The regression equation is given as d=β0+β1·A. Use the table to determine the value of β0 and β1: X = A Y = d X*Y X*X 23 570 13110 529 27 520 14040 729 28 455 12740 784 40 455 18200 1600 52 455 23660 2704 64 350 22400 4096 65 425 27625 4225 70 375 26250 4900 Sum 369 3605 158025 19567 β0=∑Y·∑X2-∑X·∑XYn·∑X2-∑X2=(3605)·(19567)-(369)·(158025)8·(19567)-3692=600.1β1=n·∑XY-∑X·∑Yn·∑X2-∑X2=(8)·(158025)-(369)·(3605)8·(19567)-3692 =-3.241 The regression equation is d=600.1-3.241·A.Draw the line of best fit on the graph: B) Two chosen points on the regression line are (25, 520) and (55, 425). C) Determine line of best fit using the above two points: y-y1x-x1=y2-y1x2-x1d-520A-25=425-52055-25d-520A-25=-9530d-520A-25=-1966d-520=-19A-256d-3120=-19A+4756d=3120+475-19A6d=3595-19Ad=3595-19A6d=599.17-3.17·A The equation for our line of best fit is d = 599.17- 3.17*A.D) A=32 yearsd=599.17-3.17*A=599.17-3.17*32=599.17-101.333=497.84=498 feet The estimated distance at which someone can clearly read a road sign when they are 32 years old is 498 feet.