Chapter 11 : Air pollution and mortality study |
Data Listing |
Obs | city | MORT | PRECIP | EDUC | NONWHITE | NOX | SO2 |
---|---|---|---|---|---|---|---|
1 | Akron, OH | 921.87 | 36 | 11.4000 | 8.8000 | 15 | 59 |
2 | Albany, NY | 997.88 | 35 | 11.0000 | 3.5000 | 10 | 39 |
3 | Allentown, PA | 962.35 | 44 | 9.8000 | 0.8000 | 6 | 33 |
4 | Atlanta, GA | 982.29 | 47 | 11.1000 | 27.1000 | 8 | 24 |
5 | Baltimore, MD | 1071.29 | 43 | 9.6000 | 24.4000 | 38 | 206 |
6 | Birmingham, AL | 1030.38 | 53 | 10.2000 | 38.5000 | 32 | 72 |
7 | Boston, MA | 934.70 | 43 | 12.1000 | 3.5000 | 32 | 62 |
8 | Bridgeport, CT | 899.53 | 45 | 10.6000 | 5.3000 | 4 | 4 |
9 | Buffalo, NY | 1001.90 | 36 | 10.5000 | 8.1000 | 12 | 37 |
10 | Canton, OH | 912.35 | 36 | 10.7000 | 6.7000 | 7 | 20 |
11 | Chattanooga, TN | 1017.61 | 52 | 9.6000 | 22.2000 | 8 | 27 |
12 | Chicago, IL | 1024.89 | 33 | 10.9000 | 16.3000 | 63 | 278 |
13 | Cincinnati, OH | 970.47 | 40 | 10.2000 | 13.0000 | 26 | 146 |
14 | Cleveland, OH | 985.95 | 35 | 11.1000 | 14.7000 | 21 | 64 |
15 | Columbus, OH | 958.84 | 37 | 11.9000 | 13.1000 | 9 | 15 |
16 | Dallas, TX | 860.10 | 35 | 11.8000 | 14.8000 | 1 | 1 |
17 | Dayton, OH | 936.23 | 36 | 11.4000 | 12.4000 | 4 | 16 |
18 | Denver, CO | 871.77 | 15 | 12.2000 | 4.7000 | 8 | 28 |
19 | Detroit, MI | 959.22 | 31 | 10.8000 | 15.8000 | 35 | 124 |
20 | Flint, MI | 941.18 | 30 | 10.8000 | 13.1000 | 4 | 11 |
21 | Fort Worth, TX | 891.71 | 31 | 11.4000 | 11.5000 | 1 | 1 |
22 | Grand Rapids, MI | 871.34 | 31 | 10.9000 | 5.1000 | 3 | 10 |
23 | Greeensboro, NC | 971.12 | 42 | 10.4000 | 22.7000 | 3 | 5 |
24 | Hartford, CT | 887.47 | 43 | 11.5000 | 7.2000 | 3 | 10 |
25 | Houston, TX | 952.53 | 46 | 11.4000 | 21.0000 | 5 | 1 |
26 | Indianapolis, IN | 968.66 | 39 | 11.4000 | 15.6000 | 7 | 33 |
27 | Kansas City, MO | 919.73 | 35 | 12.0000 | 12.6000 | 4 | 4 |
28 | Lancaster, PA | 844.05 | 43 | 9.5000 | 2.9000 | 7 | 32 |
29 | Los Angeles, CA | 861.83 | 11 | 12.1000 | 7.8000 | 319 | 130 |
30 | Louisville, KY | 989.27 | 30 | 9.9000 | 13.1000 | 37 | 193 |
31 | Memphis, TN | 1006.49 | 50 | 10.4000 | 36.7000 | 18 | 34 |
32 | Miami, FL | 861.44 | 60 | 11.5000 | 13.5000 | 1 | 1 |
33 | Milwaukee, WI | 929.15 | 30 | 11.1000 | 5.8000 | 23 | 125 |
34 | Minneapolis, MN | 857.62 | 25 | 12.1000 | 2.0000 | 11 | 26 |
35 | Nashville, TN | 961.01 | 45 | 10.1000 | 21.0000 | 14 | 78 |
36 | New Haven, CT | 923.23 | 46 | 11.3000 | 8.8000 | 3 | 8 |
37 | New Orleans, LA | 1113.06 | 54 | 9.7000 | 31.4000 | 17 | 1 |
38 | New York, NY | 994.65 | 42 | 10.7000 | 11.3000 | 26 | 108 |
39 | Philadelphia, PA | 1015.02 | 42 | 10.5000 | 17.5000 | 32 | 161 |
40 | Pittsburgh, PA | 991.29 | 36 | 10.6000 | 8.1000 | 59 | 263 |
41 | Portland, OR | 893.99 | 37 | 12.0000 | 3.6000 | 21 | 44 |
42 | Providence, RI | 938.50 | 42 | 10.1000 | 2.2000 | 4 | 18 |
43 | Reading, PA | 946.18 | 41 | 9.6000 | 2.7000 | 11 | 89 |
44 | Richmond, VA | 1025.50 | 44 | 11.0000 | 28.6000 | 9 | 48 |
45 | Rochester, NY | 874.28 | 32 | 11.1000 | 5.0000 | 4 | 18 |
46 | Saint Louis, MO | 953.56 | 34 | 9.7000 | 17.2000 | 15 | 68 |
47 | San Diego, CA | 839.71 | 10 | 12.1000 | 5.9000 | 66 | 20 |
48 | San Francisco, CA | 911.70 | 18 | 12.2000 | 13.7000 | 171 | 86 |
49 | San Jose, CA | 790.73 | 13 | 12.2000 | 3.0000 | 32 | 3 |
50 | Seattle, WA | 899.26 | 35 | 12.2000 | 5.7000 | 7 | 20 |
51 | Springfield, MA | 904.16 | 45 | 11.1000 | 3.4000 | 4 | 20 |
52 | Syracuse, NY | 950.67 | 38 | 11.4000 | 3.8000 | 5 | 25 |
53 | Toledo, OH | 972.46 | 31 | 10.7000 | 9.5000 | 7 | 25 |
54 | Utica, NY | 912.20 | 40 | 10.3000 | 2.5000 | 2 | 11 |
55 | Washington, DC | 967.80 | 41 | 12.3000 | 25.9000 | 28 | 102 |
56 | Wichita, KS | 823.76 | 28 | 12.1000 | 7.5000 | 2 | 1 |
57 | Wilmington, DE | 1003.50 | 45 | 11.3000 | 12.1000 | 11 | 42 |
58 | Worcester, MA | 895.70 | 45 | 11.1000 | 1.0000 | 3 | 8 |
59 | York, PA | 911.82 | 42 | 9.0000 | 4.8000 | 8 | 49 |
60 | Youngstown, OH | 954.44 | 38 | 10.7000 | 11.7000 | 13 | 39 |
Chapter 11 : Air pollution and mortality study |
Fit of Air Pollution with REG |
Number of Observations Read | 60 |
---|---|
Number of Observations Used | 60 |
Analysis of Variance | |||||
---|---|---|---|---|---|
Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
Model | 5 | 152888 | 30578 | 21.90 | <.0001 |
Error | 54 | 75385 | 1396.01827 | ||
Corrected Total | 59 | 228273 |
Root MSE | 37.36333 | R-Square | 0.6698 |
---|---|---|---|
Dependent Mean | 940.35677 | Adj R-Sq | 0.6392 |
Coeff Var | 3.97331 |
Parameter Estimates | ||||||
---|---|---|---|---|---|---|
Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| | Variance Inflation |
Intercept | 1 | 1000.10208 | 92.39811 | 10.82 | <.0001 | 0 |
PRECIP | 1 | 1.37920 | 0.70000 | 1.97 | 0.0539 | 2.06457 |
EDUC | 1 | -15.07895 | 7.07060 | -2.13 | 0.0375 | 1.50971 |
NONWHITE | 1 | 3.16024 | 0.62874 | 5.03 | <.0001 | 1.32969 |
NOX | 1 | -0.10756 | 0.13589 | -0.79 | 0.4321 | 1.67530 |
SO2 | 1 | 0.35541 | 0.09140 | 3.89 | 0.0003 | 1.41859 |
Chapter 11 : Air pollution and mortality study |
Fit of Air Pollution with REG |
Number of Observations Read | 60 |
---|---|
Number of Observations Used | 60 |
Analysis of Variance | |||||
---|---|---|---|---|---|
Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
Model | 4 | 152013 | 38003 | 27.41 | <.0001 |
Error | 55 | 76260 | 1386.54072 | ||
Corrected Total | 59 | 228273 |
Root MSE | 37.23628 | R-Square | 0.6659 |
---|---|---|---|
Dependent Mean | 940.35677 | Adj R-Sq | 0.6416 |
Coeff Var | 3.95980 |
Parameter Estimates | |||||
---|---|---|---|---|---|
Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
Intercept | 1 | 999.31617 | 92.07861 | 10.85 | <.0001 |
PRECIP | 1 | 1.61112 | 0.63358 | 2.54 | 0.0138 |
EDUC | 1 | -15.77337 | 6.99211 | -2.26 | 0.0281 |
NONWHITE | 1 | 3.06093 | 0.61400 | 4.99 | <.0001 |
SO2 | 1 | 0.32718 | 0.08387 | 3.90 | 0.0003 |
Chapter 11 : Air pollution and mortality study |
Fit of Air Pollution with REG |
Obs | city | resid | yhat | student | rstudent | cookd | leverage | dffits |
---|---|---|---|---|---|---|---|---|
1 | Akron, OH | -1.8702 | 923.74 | -0.05086 | -0.05039 | 0.00001 | 0.02477 | -0.00803 |
2 | Albany, NY | 92.2032 | 905.67 | 2.51726 | 2.65170 | 0.04242 | 0.03239 | 0.48513 |
3 | Allentown, PA | 33.4816 | 928.87 | 0.94701 | 0.94611 | 0.01960 | 0.09849 | 0.31272 |
4 | Atlanta, GA | -8.4670 | 990.76 | -0.23713 | -0.23509 | 0.00098 | 0.08050 | -0.06956 |
5 | Baltimore, MD | 12.0326 | 1059.26 | 0.34990 | 0.34709 | 0.00422 | 0.14708 | 0.14413 |
6 | Birmingham, AL | -34.8401 | 1065.22 | -1.02756 | -1.02810 | 0.04353 | 0.17090 | -0.46676 |
7 | Boston, MA | 25.9647 | 908.74 | 0.74803 | 0.74499 | 0.01688 | 0.13104 | 0.28930 |
8 | Bridgeport, CT | -22.6217 | 922.15 | -0.62458 | -0.62108 | 0.00444 | 0.05389 | -0.14824 |
9 | Buffalo, NY | 73.3065 | 928.60 | 2.00124 | 2.05936 | 0.02671 | 0.03227 | 0.37607 |
10 | Canton, OH | -3.2465 | 915.59 | -0.08864 | -0.08784 | 0.00005 | 0.03260 | -0.01613 |
11 | Chattanooga, TN | 9.1562 | 1008.46 | 0.25757 | 0.25537 | 0.00129 | 0.08862 | 0.07963 |
12 | Chicago, IL | 3.4817 | 1021.40 | 0.10737 | 0.10640 | 0.00073 | 0.24169 | 0.06007 |
13 | Cincinnati, OH | -19.9664 | 990.43 | -0.55311 | -0.54959 | 0.00392 | 0.06019 | -0.13908 |
14 | Cleveland, OH | 39.3936 | 946.56 | 1.06934 | 1.07077 | 0.00496 | 0.02122 | 0.15766 |
15 | Columbus, OH | 42.6084 | 916.23 | 1.17057 | 1.17460 | 0.01274 | 0.04442 | 0.25325 |
16 | Dallas, TX | -55.1076 | 915.21 | -1.51545 | -1.53398 | 0.02231 | 0.04631 | -0.33804 |
17 | Dayton, OH | 15.5434 | 920.69 | 0.42299 | 0.41981 | 0.00096 | 0.02613 | 0.06877 |
18 | Denver, CO | 17.1706 | 854.60 | 0.48902 | 0.48561 | 0.00596 | 0.11082 | 0.17144 |
19 | Detroit, MI | -8.6209 | 967.84 | -0.23739 | -0.23534 | 0.00058 | 0.04882 | -0.05332 |
20 | Flint, MI | 20.1864 | 920.99 | 0.55930 | 0.55577 | 0.00403 | 0.06050 | 0.14103 |
21 | Fort Worth, TX | -13.2644 | 904.97 | -0.36381 | -0.36092 | 0.00114 | 0.04127 | -0.07488 |
22 | Grand Rapids, MI | -24.8758 | 896.21 | -0.68357 | -0.68022 | 0.00439 | 0.04487 | -0.14744 |
23 | Greeensboro, NC | -2.9373 | 974.06 | -0.08190 | -0.08116 | 0.00010 | 0.07241 | -0.02268 |
24 | Hartford, CT | -25.0452 | 912.51 | -0.69075 | -0.68743 | 0.00522 | 0.05185 | -0.16075 |
25 | Houston, TX | -5.6891 | 958.22 | -0.15793 | -0.15652 | 0.00034 | 0.06409 | -0.04096 |
26 | Indianapolis, IN | 27.7839 | 940.88 | 0.75681 | 0.75383 | 0.00330 | 0.02796 | 0.12786 |
27 | Kansas City, MO | 13.4275 | 906.30 | 0.36982 | 0.36690 | 0.00142 | 0.04924 | 0.08350 |
28 | Lancaster, PA | -94.0410 | 938.09 | -2.67375 | -2.84035 | 0.17276 | 0.10780 | -0.98731 |
29 | Los Angeles, CA | -30.7567 | 892.59 | -0.89885 | -0.89726 | 0.02977 | 0.15555 | -0.38510 |
30 | Louisville, KY | -5.4728 | 994.74 | -0.15747 | -0.15607 | 0.00073 | 0.12887 | -0.06003 |
31 | Memphis, TN | -32.7995 | 1039.29 | -0.96088 | -0.96019 | 0.03508 | 0.15964 | -0.41850 |
32 | Miami, FL | -94.8005 | 956.24 | -2.81722 | -3.01770 | 0.35633 | 0.18333 | -1.42977 |
33 | Milwaukee, WI | -2.0666 | 931.22 | -0.05702 | -0.05650 | 0.00004 | 0.05255 | -0.01331 |
34 | Minneapolis, MN | -5.7431 | 863.37 | -0.15925 | -0.15783 | 0.00034 | 0.06198 | -0.04057 |
35 | Nashville, TN | -41.2964 | 1002.31 | -1.13568 | -1.13873 | 0.01254 | 0.04636 | -0.25108 |
36 | New Haven, CT | -1.5084 | 924.74 | -0.04166 | -0.04128 | 0.00002 | 0.05436 | -0.00990 |
37 | New Orleans, LA | 83.3006 | 1029.76 | 2.43113 | 2.54983 | 0.21397 | 0.15327 | 1.08484 |
38 | New York, NY | 26.5155 | 968.13 | 0.72660 | 0.72344 | 0.00435 | 0.03954 | 0.14679 |
39 | Philadelphia, PA | 7.4175 | 1007.61 | 0.20691 | 0.20510 | 0.00068 | 0.07315 | 0.05762 |
40 | Pittsburgh, PA | -9.6714 | 1000.96 | -0.29641 | -0.29394 | 0.00531 | 0.23218 | -0.16164 |
41 | Portland, OR | -1.0717 | 895.06 | -0.02985 | -0.02958 | 0.00001 | 0.07064 | -0.00816 |
42 | Providence, RI | 18.2043 | 920.30 | 0.50795 | 0.50450 | 0.00410 | 0.07366 | 0.14226 |
43 | Reading, PA | -5.1466 | 951.33 | -0.14544 | -0.14414 | 0.00045 | 0.09685 | -0.04720 |
44 | Richmond, VA | 25.5562 | 999.95 | 0.71597 | 0.71276 | 0.00905 | 0.08110 | 0.21174 |
45 | Rochester, NY | -22.7007 | 896.98 | -0.62020 | -0.61670 | 0.00269 | 0.03377 | -0.11529 |
46 | Saint Louis, MO | -22.4290 | 975.99 | -0.63473 | -0.63125 | 0.00890 | 0.09945 | -0.20977 |
47 | San Diego, CA | -9.4638 | 849.17 | -0.27838 | -0.27604 | 0.00310 | 0.16649 | -0.12337 |
48 | San Francisco, CA | 5.7473 | 905.95 | 0.16343 | 0.16198 | 0.00065 | 0.10811 | 0.05639 |
49 | San Jose, CA | -47.2571 | 837.99 | -1.36711 | -1.37824 | 0.05996 | 0.13822 | -0.55198 |
50 | Seattle, WA | 12.0026 | 887.26 | 0.33326 | 0.33055 | 0.00153 | 0.06449 | 0.08679 |
51 | Springfield, MA | -9.5281 | 913.68 | -0.26467 | -0.26242 | 0.00098 | 0.06528 | -0.06935 |
52 | Syracuse, NY | 50.1384 | 900.53 | 1.37476 | 1.38623 | 0.01604 | 0.04070 | 0.28552 |
53 | Toledo, OH | 54.7197 | 917.74 | 1.50326 | 1.52110 | 0.02099 | 0.04437 | 0.32778 |
54 | Utica, NY | -0.3447 | 912.55 | -0.00957 | -0.00948 | 0.00000 | 0.06324 | -0.00246 |
55 | Washington, DC | -16.2074 | 984.01 | -0.47334 | -0.46998 | 0.00818 | 0.15444 | -0.20086 |
56 | Wichita, KS | -53.0900 | 876.85 | -1.46715 | -1.48306 | 0.02536 | 0.05563 | -0.35994 |
57 | Wilmington, DE | 59.1455 | 944.36 | 1.62322 | 1.64836 | 0.02337 | 0.04246 | 0.34710 |
58 | Worcester, MA | -6.7148 | 902.41 | -0.18807 | -0.18642 | 0.00062 | 0.08068 | -0.05522 |
59 | York, PA | -43.9304 | 955.75 | -1.27716 | -1.28469 | 0.05608 | 0.14669 | -0.53265 |
60 | Youngstown, OH | 14.1052 | 940.34 | 0.38281 | 0.37982 | 0.00062 | 0.02084 | 0.05541 |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of resid*yhat. Symbol is value of city. resid | | 100 + | A | N | B | | T W 50 + S | C C | A | B I N R | D K DF Y | S S C B 0 +-------------------------P------UC--A-M---------------G----------------C-------------------- | S M W S R H D AL P | F W C | G H B S | L M B | Y N -50 + S W | D | | | | L M -100 + | -+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+- 825 850 875 900 925 950 975 1000 1025 1050 1075 yhat NOTE: 4 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of student*yhat. Symbol is value of city. student | 3 + | |--------------------------------A-------------------------------------------------------- | N | 2 +--------------------------------------B-------------------------------------------------- | | T W | S | C 1 + A C | B I N R | F | D S K D Y B | S C C 0 + P C A M G | S M W S R H D A LP | F W | G H B S C | L -1 + M B | Y N | S W | D | -2 +----------------------------------------------------------------------------------------- | | |-----------------------------------------L----------------------------------------------- | M -3 + | ---+-------------+-------------+-------------+-------------+-------------+-------------+-- 800 850 900 950 1000 1050 1100 yhat NOTE: 5 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of rstudent*yhat. Symbol is value of city. rstudent | 3 + | |--------------------------------A---------------------------------N---------------------- | | 2 +--------------------------------------B-------------------------------------------------- | | T W | S | C 1 + A C | B I N R | F | D S K D Y B | S C C 0 + P C A M G | S M W S R H D A LP | F W | G H B S C | L -1 + M B | Y N | S W | D | -2 +----------------------------------------------------------------------------------------- | | |----------------------------------------------------------------------------------------- | L -3 + M | ---+-------------+-------------+-------------+-------------+-------------+-------------+-- 800 850 900 950 1000 1050 1100 yhat NOTE: 5 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of leverage*yhat. Symbol is value of city. leverage | 0.25 + | C | P | | | 0.20 + | |----------------------------------------------M------------------------------------------ | B | S | L W M 0.15 + Y N B | S | B | L | | D S L 0.10 + A R S | C | W A R | P G P | S P S H | M W FN C 0.05 + K D B M D N | GSF C W N | R A C B | DA I C | | 0.00 + | ---+-------------+-------------+-------------+-------------+-------------+-------------+-- 800 850 900 950 1000 1050 1100 yhat NOTE: 4 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of cookd*yhat. Symbol is value of city. cookd | 1.0 +-------------------------------------------------------------------------------------------- | | | | | 0.8 + | | | | | 0.6 + | | | | | 0.4 + | M | | | | 0.2 + N | L | | | S Y | W L AB DT A W M B 0.0 + S D M S PGSWF HCDBA M I CR H DN G W AL PN C C B | -+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+- 825 850 875 900 925 950 975 1000 1025 1050 1075 yhat NOTE: 15 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Plot of dffits*yhat. Symbol is value of city. dffits | 1.5 + | | | | N 1.0 +------------------------------------------------------------------------------------------- | | | | 0.5 + A | B | S B C A W | D C R | S K DF I N C C B 0.0 + M P UC A M R H G | S G WF S B D AL | H S W P | D N | W L M -0.5 + Y B | S | | | -1.0 + L | | | | M -1.5 + | -+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+ 825 850 875 900 925 950 975 1000 1025 1050 1075 yhat NOTE: 8 obs hidden. |
Chapter 11 : Air pollution and mortality study |
Various plot with group variable |
Moments | |||
---|---|---|---|
N | 60 | Sum Weights | 60 |
Mean | 0 | Sum Observations | 0 |
Std Deviation | 35.951884 | Variance | 1292.53796 |
Skewness | 0.0312791 | Kurtosis | 1.10303795 |
Uncorrected SS | 76259.7396 | Corrected SS | 76259.7396 |
Coeff Variation | . | Std Error Mean | 4.64136826 |
Basic Statistical Measures | |||
---|---|---|---|
Location | Variability | ||
Mean | 0.00000 | Std Deviation | 35.95188 |
Median | -2.50195 | Variance | 1293 |
Mode | . | Range | 187.00371 |
Interquartile Range | 38.88520 |
Tests for Location: Mu0=0 | ||||
---|---|---|---|---|
Test | Statistic | p Value | ||
Student's t | t | 0 | Pr > |t| | 1.0000 |
Sign | M | -5 | Pr >= |M| | 0.2451 |
Signed Rank | S | -21 | Pr >= |S| | 0.8787 |
Tests for Normality | ||||
---|---|---|---|---|
Test | Statistic | p Value | ||
Shapiro-Wilk | W | 0.971756 | Pr < W | 0.1777 |
Kolmogorov-Smirnov | D | 0.093961 | Pr > D | >0.1500 |
Cramer-von Mises | W-Sq | 0.110757 | Pr > W-Sq | 0.0825 |
Anderson-Darling | A-Sq | 0.640932 | Pr > A-Sq | 0.0924 |
Quantiles (Definition 5) | |
---|---|
Quantile | Estimate |
100% Max | 92.20319 |
99% | 92.20319 |
95% | 66.22597 |
90% | 46.37344 |
75% Q3 | 17.68746 |
50% Median | -2.50195 |
25% Q1 | -21.19774 |
10% | -42.61341 |
5% | -54.09883 |
1% | -94.80052 |
0% Min | -94.80052 |
Extreme Observations | |||
---|---|---|---|
Lowest | Highest | ||
Value | Obs | Value | Obs |
-94.8005 | 32 | 54.7197 | 53 |
-94.0410 | 28 | 59.1455 | 57 |
-55.1076 | 16 | 73.3065 | 9 |
-53.0900 | 56 | 83.3006 | 37 |
-47.2571 | 49 | 92.2032 | 2 |
Stem Leaf # Boxplot Normal Probability Plot 9 2 1 0 95+ * 8 3 1 0 | * +++ 7 3 1 | | * +++ 6 | | +++ 5 059 3 | | **+* 4 3 1 | | *+ 3 39 2 | | ++* 2 06678 5 | | ++*** 1 2234678 7 +-----+ | +**** 0 3679 4 | + | | ++*** -0 998766553322210 15 *-----* | ******** -1 6300 4 | | | **++ -2 553320 6 +-----+ | ***+ -3 531 3 | | **+ -4 741 3 | | *** -5 53 2 | | **++ -6 | +++ -7 | +++ -8 |+++ -9 54 2 0 -95+ * * ----+----+----+----+ +----+----+----+----+----+----+----+----+----+----+ Multiply Stem.Leaf by 10**+1 -2 -1 0 +1 +2 |