Question

In: Statistics and Probability

Use the Tornadoes data. Your TASK is to use the months of July and August to...

Use the Tornadoes data. Your TASK is to use the months of July and August to predict the tornado activity in October. Answer questions 5 to 7. Choose the best fitting answer. Note: numbers are truncated unless specified.

5. If July had 100 tornadoes and August had 200 tornadoes, what would be your prediction for the number of tornadoes in October?

a. 34.88
b. 39.18
c. 44.15
d. 58.62

6. What is the approximate error of this prediction?

a. 8.44
b. 12.33
c. 20.15
d. 36.00

7. The intercept here has a value of 5.17. What is the STATISTICAL interpretation of this number?

a. This is the predicted number of tornadoes in October when July and August have 100 and 200 tornadoes, respectively.
b. It is meaningless.
c. This is the predicted number of tornadoes in October when July and August have zero tornadoes.
d. The number of tornadoes in October is zero when July and August have 100 and 200 tornadoes, respectively.

Tornadoes and Deaths by Year and Month (1950-1994)                                                                                                                                                                                                              
                                                                                                                                                                                                                
Year    Total Tornadoes Tornadoes by Month                                                                                              Total Deaths    Deaths by Month                                                                                 
                Jan     Feb     Mar     Apr     May     June    July    Aug     Sept    Oct     Nov     Dec             Jan     Feb     Mar     Apr     May     June    July    Aug     Sept    Oct     Nov     Dec
1950    201     7       20      21      15      61      28      23      13      3       2       4       4       70      1       45      1       12      2       6       0       0       0       0       0       3
1951    260     2       10      6       26      57      76      23      27      9       2       12      10      34      0       1       0       2       7       9       5       0       8       0       1       1
1952    240     12      27      43      37      34      34      27      16      1       0       6       3       230     0       10      209     4       2       2       2       1       0       0       0       0
1953    422     14      16      40      47      94      111     32      24      5       6       12      21      519     0       3       24      36      163     244     0       0       0       0       0       49
1954    550     2       17      62      113     101     107     45      49      21      14      2       17      36      0       2       10      2       9       5       0       1       3       2       0       2
1955    593     3       4       43      99      148     153     49      33      15      23      20      3       129     0       0       5       7       106     2       5       0       2       1       1       0
1956    504     2       47      31      85      79      65      92      42      16      29      7       9       83      0       8       1       67      4       0       1       2       0       0       0       0
1957    858     17      5       38      216     228     147     55      20      17      18      59      38      193     13      0       1       30      87      14      0       0       2       2       25      19
1958    564     11      20      15      76      68      128     121     46      24      9       45      1       67      0       13      0       4       0       43      1       1       1       4       0       0
1959    604     16      20      43      30      226     73      63      38      58      24      11      2       58      3       21      9       1       8       2       0       0       14      0       0       0
1960    616     9       28      28      70      201     125     42      48      21      18      25      1       46      0       0       0       7       34      3       0       1       0       1       0       0
1961    697     1       31      124     74      137     107     77      27      53      14      36      16      52      0       0       7       4       23      2       0       0       15      0       1       0
1962    657     12      25      37      41      200     171     78      51      24      11      5       2       30      1       0       17      2       4       0       0       6       0       0       0       0
1963    463     15      6       48      84      71      90      62      26      33      13      15      0       31      1       0       8       16      1       0       0       2       3       0       0       0
1964    704     14      2       36      157     134     137     63      79      25      22      17      18      73      10      0       6       15      16      0       0       2       0       22      0       2
1965    897     21      32      34      123     273     147     85      61      64      16      34      7       301     0       0       2       268     17      7       0       1       0       1       5       0
1966    585     1       28      12      80      98      126     100     58      22      29      20      11      98      0       0       58      12      0       19      3       0       0       6       0       0
1967    926     39      8       42      149     116     210     90      28      139     36      8       61      114     7       0       3       73      3       6       1       2       5       4       0       10
1968    660     5       7       28      102     145     136     56      66      25      14      44      32      131     0       0       0       40      72      11      2       2       0       0       3       1
1969    608     3       5       8       68      145     137     98      70      20      26      5       23      66      32      0       1       2       4       7       0       19      0       0       0       1
1970    654     9       16      25      117     88      134     82      55      54      50      10      14      73      0       0       2       30      26      6       3       0       0       6       0       0
1971    889     19      83      40      75      166     199     100     50      47      38      16      56      159     1       134     2       11      7       1       1       0       0       0       0       2
1972    741     33      7       69      96      140     114     115     59      49      34      17      8       27      5       0       0       16      0       2       0       2       0       0       2       0
1973    1102    33      10      80      150     250     224     80      51      69      25      81      49      89      1       0       17      10      35      3       1       4       3       0       12      3
1974    945     24      23      36      267     144     194     59      107     25      45      13      8       366     2       0       1       317     10      31      0       0       0       5       0       0
1975    919     52      45      84      108     188     196     79      60      34      12      39      22      60      12      7       12      13      5       6       2       2       0       0       0       1
1976    834     12      36      180     113     155     169     84      38      35      11      0       1       44      0       5       21      1       8       3       2       1       3       0       0       0
1977    852     5       17      64      88      228     132     99      82      65      25      24      23      43      0       2       0       26      4       0       1       6       1       1       0       2
1978    789     23      7       17      107     213     148     143     65      20      7       9       30      53      2       0       0       4       7       17      11      1       6       0       0       5
1979    855     16      4       53      123     112     150     132     126     69      47      21      2       84      0       0       1       58      2       8       1       5       2       7       0       0
1980    866     5       11      41      137     203     217     95      73      37      43      3       1       28      0       0       2       4       8       7       5       0       1       1       0       0
1981    782     2       25      33      84      187     223     98      64      26      32      7       1       24      0       2       1       13      0       8       0       0       0       0       0       0
1982    1047    18      3       60      150     329     196     95      34      38      9       19      96      64      1       0       6       30      14      4       0       0       2       0       0       7
1983    931     13      41      71      65      249     178     99      76      19      13      49      58      34      2       1       0       6       14      2       4       0       0       0       0       5
1984    907     1       27      73      176     169     242     72      47      17      49      30      4       122     0       0       64      33      6       14      0       0       0       4       1       0
1985    684     2       7       38      134     182     82      51      108     40      18      19      3       94      0       0       2       5       78      3       0       3       0       0       3       0
1986    765     0       30      76      84      173     134     88      67      65      26      17      5       15      0       2       6       2       1       0       3       1       0       0       0       0
1987    656     6       19      38      20      126     132     163     63      19      1       55      14      59      0       6       1       1       31      2       0       1       0       0       11      6
1988    702     17      4       28      58      132     63      103     61      76      19      121     20      32      5       0       1       4       3       0       0       3       1       0       14      1
1989    856     14      18      43      82      231     252     59      36      31      30      57      3       50      0       0       1       0       9       5       0       0       0       4       31      0
1990    1133    11      57      86      108     243     329     106     60      45      35      18      35      53      0       1       3       0       5       11      0       29      0       2       0       2
1991    1132    29      11      157     204     335     216     64      46      26      21      20      3       39      1       0       13      21      0       1       1       0       0       0       2       0
1992    1297    15      29      55      53      137     399     213     115     81      34      146     20      39      0       0       5       0       0       1       0       3       0       4       26      0
1993    1173    17      34      48      85      177     313     242     112     65      55      19      6       33      0       3       5       10      2       1       0       6       2       4       0       0
1994    1082    13      9       58      205     161     234     155     120     30      51      42      4       69      0       0       40      12      0       3       3       4       0       0       7       0

Expert Solution

I used R software to solve this problem.

R codes:

> oct=scan('clipboard')
Read 45 items
> oct
[1] 2 2 0 6 14 23 29 18 9 24 18 14 11 13 22 16 29 36 14 26 50 38 34 25 45
[26] 12 11 25 7 47 43 32 9 13 49 18 26 1 19 30 35 21 34 55 51
> july=scan('clipboard')
Read 45 items
> july
[1] 23 23 27 32 45 49 92 55 121 63 42 77 78 62 63 85 100 90 56
[20] 98 82 100 115 80 59 79 84 99 143 132 95 98 95 99 72 51 88 163
[39] 103 59 106 64 213 242 155
> aug=scan('clipboard')
Read 45 items
> aug
[1] 13 27 16 24 49 33 42 20 46 38 48 27 51 26 79 61 58 28 66
[20] 70 55 50 59 51 107 60 38 82 65 126 73 64 34 76 47 108 67 63
[39] 61 36 60 46 115 112 120
> fit=lm(oct~july+aug)
> fit

Call:
lm(formula = oct ~ july + aug)

Coefficients:
(Intercept) july aug

5.17440 0.04855 0.24299

5.

If July had 100 tornadoes and August had 200 tornadoes then October has,

Oct = 5.1744 + 0.04855 July + 0.24299 August

= 5.1744 + 0.04855 * 100 + 0.24299 * 200

= 58.6274

6.

In order to find error we have to know its actual value.

error = actual value - predicted value

7.

This is the predicted number of tornadoes in October when July and August have zero tornadoes.

orchestra answered 2 years ago

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