Ted Williams was famous for almost always swinging at the first pitch each time
ID: 3323103 • Letter: T
Question
Ted Williams was famous for almost always swinging at the first pitch each time he came up to the plate. He claimed that one of the reasons he could hit so well was because of his visual acuity and that he could even see the threads on the baseball as it was coming toward home plate. One of the more interesting details about his personal life is that despite his request to be cremated after death, his children saw to it that his body was placed in cryogenic frozen stasis in case medical science ever advanced to the point of realistic human cloning. This time, Ted's number of "runs batted in" are listed (on the left) for each complete season he played. You will also notice Runs Batted In All Time Leaders Top 1,090 (on the right) that he is in 14th position for "all time leaders" irn career RBls having recorded 1,839 total. 2.213 3 Note: this total is different than what is listed on the left simply because it includes Ae Redrigus the partial seasons he played in 1952 and 1953 in which he accumulated 37 other "runs batted in" or RBls. In your analysis, do not include these two partial seasons)) Los er 2.00 Stan Musal y Cobe 1$377 Avtrage a) Using your regression tools of your calculator, place the data (years, RBIs) into your list editor. Make a rough scatterplot in the box below: Cap Anson 844 13 Ted Williams Career R (Runs Batted in b) Now, calculate the least-squares regression line for these complete seasons. Sketch the line in your graph above. Using two decimals for the linear equation, r, and fill in the following: least-squares line: c) Next, use your calculator to interpolate (using two decimals in the table below), the RBls Ted Williams could have potentially recorded during the missing war years had he have not gone to war. d) Now, to the nearest whole number, what would have been his career RBI total? e) What historical position (rank) would this projection have place him into regarding the all-time leader board for RBIs?- Missing War Years Briefly comment on which of the two statistical interpolations (home runs vs. RBIs) you would have greater confidence in making and why: 1943 TotalExplanation / Answer
a)Plot the graph manually. Just for reference not involved in calculations
b)
X
Y
X^2
Y^2
XY
1939
145
3759721
21025
281155
1940
123
3763600
15129
238620
1941
120
3767481
14400
232920
1942
127
3771364
16129
246634
1946
123
3786916
15129
239358
1947
114
3790809
12996
221958
1948
127
3794704
16129
247396
1949
159
3798601
25281
309891
1950
97
3802500
9409
189150
1951
126
3806401
15876
245826
1954
89
3818116
7921
173906
1955
83
3822025
6889
162265
1956
82
3825936
6724
160392
1957
87
3829849
7569
170259
1958
85
3833764
7225
166430
1959
43
3837681
1849
84237
1960
72
3841600
5184
141120
Total
33152
1802
64651068
204864
3511517
Y = a + bX
N= 17
Thus,
a = (1802)(64651068)-(33152)(3511517)/(17(64651068)-( 33152)^2) = 87412952/13052 = 6697.28
b = (17(3511517))-( 33152)( 1802)/ (17(64651068)-( 33152)^2) = -44115/13052 = -3.38
Thus , Y = -3.38X + 6697.28
c)For missing years we can obtains the value by using equation
Y = -3.38X + 6697.28 and substituting X as missing years
Thus,
X
Y = -3.38X + 6697.28
1943
129.94
1944
126.56
1945
123.18
1952
99.52
1953
96.14
d)Carrer RBI total including missing years = 1802+129.94+126.56+123.18+99.52+96.14
= 2377.34= approx 2377
e)Historical rank would have been 1 (as 2377 will be new top score)
X
Y
X^2
Y^2
XY
1939
145
3759721
21025
281155
1940
123
3763600
15129
238620
1941
120
3767481
14400
232920
1942
127
3771364
16129
246634
1946
123
3786916
15129
239358
1947
114
3790809
12996
221958
1948
127
3794704
16129
247396
1949
159
3798601
25281
309891
1950
97
3802500
9409
189150
1951
126
3806401
15876
245826
1954
89
3818116
7921
173906
1955
83
3822025
6889
162265
1956
82
3825936
6724
160392
1957
87
3829849
7569
170259
1958
85
3833764
7225
166430
1959
43
3837681
1849
84237
1960
72
3841600
5184
141120
Total
33152
1802
64651068
204864
3511517
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