Honors Statistics. Tuesday March 1, Aug 23-8:26 PM. 2. Please find folder and take your seat. 4. Exploring coefficient of determination

Transcription

1 Honors Statistics Tuesday March 1, 2016 Aug 23-8:26 PM 1. Welcome to class 2. Please find folder and take your seat. 3. Review OTL C3#8 4. Exploring coefficient of determination 5. Exploring computer outputs 6. Collect folders Aug 23-8:31 PM 1

2 Feb 28-3:45 PM Oct 1-9:05 AM 2

3 calc Sentence Sentence calc Sentence calc calc Sentence calc 3.13 Sentence Sep 26-11:13 AM A Skip 52 pg 195: 54 pg 196: 61aONLY then pg 197: 63 pg 196: 62aONLY then pg 197: 64 Please use "the correct" sentences... for r 2 and s Oct 5-6:47 PM 3

4 No because there is an obvious pattern in the residual plot therefore a line (linear model) is not the right (appropriate) choice. However... Oct 9-4:58 PM a) The scatterplot displays a moderately strong linear association between laboratory measurements and field measurements. The larger measurements are more spread out. b) All the points do not fall on the y = x line. The tendency is for the larger measurement to have smaller field measurements than laboratory measurements. c) the LSRL would have a smaller (flatter) slope and a y-intercept that is greater than 0. Oct 9-5:01 PM 4

5 While there is no curving in the residual plot there is a great fanning out. This means that a linear model is appropriate but the predictions for the larger measurements will not be as accurate. Oct 9-5:05 PM Given Information a) LSRL V husband height = (wife height) b) If x goes down by 1 standard deviation (1 st.dev. below x), - then y will decrease by r(s y ) standard deviations (0.5)(2.7) = inches or plug in = 62 Oct 9-5:07 PM 5

6 a) r 2 = (r) 2 25% of the variation in the height of husbands can be explained by the variation in the height of wives as calculated by the LSRL of husband height on wife height. b) s = 1.2 inches (0.5) 2 = inches is the standard deviation of the residuals. It is the typical amount the observed husband height differs from its predicted height on the LSRL. Oct 9-5:08 PM yearly index represents a percentage, likewise with January index represents a percentage b) If x goes up by 1 standard deviation, y will increase by r(s standard deviations. See the slope formula... Oct 9-5:08 PM 6

7 35.52% of the variation in the change of the stock market index for the entire year can be explained by the change in the stock market index 8.3 is the standard deviation of the residuals. It is the typical amount the observed change in the yearly stock market index Oct 9-5:08 PM Should we use a line? How good is the line at predicting y from x? How do we calculate the "error" of the prediction? Oct 3-7:38 PM 7

8 Oct 16-5:21 PM Let's examine the coefficient of Other_Explorations_and_Amusements/Least_Squares.html Oct 16-5:21 PM 8

9 If this were your data set... (in no particular order...) What is your best guess of the next number out of the bag? Oct 13-7:33 AM Oct 13-8:14 AM 9

10 Oct 13-8:14 AM Oct 19-12:23 PM 10

11 Oct 19-12:24 PM Oct 19-12:21 PM 11

12 Oct 19-12:24 PM Oct 19-12:28 PM 12

13 Oct 19-12:28 PM Feb 28-2:40 PM 13

14 Mar 1-7:24 AM Oct 23-8:57 AM 14

15 Nov 2-9:01 AM algae ^ = (temp) As the temperature increases by 1 degree F, the algae is predicted to increase by ppm = The correlation coefficient verifies the very strong positive linear association between temperature and algae level in the pond is the standard deviation of the residuals. It is the typical amount the observed algae levels differ from their predicted algae levels on the least squares regression line. Nov 2-9:01 AM 15

16 A skip 65 pg 198: use partial credit worksheet Show work for 65, 66 and 72mc, 76mc, 77mc Oct 5-6:47 PM Oct 13-7:36 AM 16

17 V a) y = x or final score = midterm score V V b) y = x V y = (50) = 67.1 V y = (100) = 87.6 c) This shows regression to the mean because the lower score is predicted to do higher (closer to the mean) and the high score is predicted to do lower (closer to the mean) see pg 184. Oct 11-10:06 PM V V b) y = x V y = (0.200) = V V a) y = x or BA season = BA early y = (0.400) = c) This shows regression to the mean because the player who hit lower is predicted to hit higher (closer to the mean) and the player who hit better is predicted to hit lower (closer to the mean) see pg 184. Oct 11-10:07 PM 17

18 A a) This is a characteristic of the correlation coefficient. Oct 11-10:08 PM A Given Information cross off c & d Oct 11-10:08 PM 18

19 C Oct 11-10:08 PM A Oct 11-10:09 PM 19

20 D Oct 11-10:09 PM A v y = x v y = (60) v y = 62.2 v y - y = = -3.2 Oct 11-10:09 PM 20

21 B v y = x v y = (120) v y = 118 v y - y = = 0 This point is exactly on the regression line. The residual is 0. Oct 11-10:09 PM E Oct 11-10:10 PM 21

22 A skip none pg 198: 70 use the LSRL worksheet examine the point (116, 41) determine its influence. Lists L RUSH, L PTSC Oct 5-6:47 PM Oct 12-7:43 PM 22

23 47.46 Jacksonville NFL 2011 Points scored Rushing yards Oct 12-7:44 PM weak positive linear association between total rushing yards and points scored in each game of the 2011 Jacksonville NFL season. Oct 12-7:45 PM 23

24 Mar 22-8:10 PM Oct 16-5:21 PM 24

25 Let's examine the coefficient of Oct 16-5:21 PM View textbook applet for means first Other_Explorations_and_Amusements/Least_Squares.html Oct 9-2:59 PM 25

26 Oct 3-8:31 PM Nov 3-8:07 PM 26

27 Oct 11-9:57 PM Oct 11-9:57 PM 27

28 Oct 23-2:18 PM Oct 23-2:09 PM 28

29 Should we use a line? How good is the line at predicting y from x? How do we calculate the "error" of the prediction? Oct 3-7:38 PM r a or (0, a) Oct 17-7:12 PM 29

30 least squares regression line of Oct 17-7:12 PM Manatees in Florida Killed Manatees Power Boat Registration 1085 The scatterplot displays a strong positive linear association between power boat registrations and the number of killed manatees V (x) Oct 8-8:49 PM 30

31 Class example Manatee data revisited Oct 3-8:56 PM Feb 28-2:00 PM 31