Aim _8 Handout _Finding the Line Of Best Fit_ - ANSWER KEY

The Bronx High School of Science, Mathematics Department Valerie Reidy, Principal Rosemarie Jahoda, A.P. Mathematics Trigonometry (M$6) Mr. J. Fox, Instructor M$6 Aim #8 Handout: Finding the Line of Best Fit 1) Is there a relationship between Math SAT scores (on a 200 – 800 scale) and the number of hours spent studying for the test? The table below shows the data collected from a study involving 20 students as they prepared for and took the Math section of the SAT. Hours Spent Studying Math SAT Score 4 390 9 580 10 650 14 730 4 410 7 530 12 600 22 790 1 350 3 400 8 590 11 640 5 450 6 520 10 690 11 690 16 770 13 700 13 730 10 640 Regression Equation (round the slope & intercept to the nearest hundredth): y = 25.33x + 353.16 a) If a student studied for 15 hours, based upon this study, what would be the expected Math SAT score? (nearest integer) ( 25.33 15 353.16 733 y = + ≈ b) If a student obtained a Math SAT score of 720, based upon this study, how many hours did the student most likely spend studying? (nearest tenth of an hour) 720 25.33 353.16 366.84 25.33 14.5 x x x hours = + → = → ≈ c) If a student spent 100 hours studying, what would be the expected Math SAT score? ( 25.33 100 353.16 2886.16 y = + ≈ barb2right OUT OF RANGE, therefore no solution!!! 1) Enter the data into list L 1 (Hours Spent Studying) and list L 2 (Math SAT score). 2) Create a scatter plot of the data by pressing 2nd Y= (STATPLOT) and choose the first plot. Turn the plot ON, set the icon to Scatter Plot (the first one), set Xlist to L 1 and Ylist to L 2 , and select a Mark of your choice. (Most of these options will already be set for you…) 3) Hit ZOOM 9: ZoomStat to see the scatter plot. 4) To find the equation for the line of best fit , press STAT, arrow right to CALC, and arrow down to 4: LinReg (ax+b). Hit ENTER. When LinReg appears on the home screen, type the parameters L 1 , L 2 , Y 1 . (To type L 1 and L 2 , press 2nd 1 and 2nd 2 . To type Y 1 , press VARS, arrow right to Y-VARS, choose 1: Function, then choose 1: Y 1 .) 5) The last parameter, Y 1 , will put the equation into Y= for you. Press Y= to see the linear regression equation . 6) Press GRAPH to see the line of best fit , also called the regression line .