Year Team Runs Singles Double Triples HR Predict Runs Error 2000 Anaheim Angels

Question

Year Team Runs Singles Double Triples HR Predict Runs Error 2000 Anaheim Angels 864 995 309 34 236 2000 Baltimore Orioles 794 992 310 22 184 2000 Boston Red Sox 792 988 316 32 167 2000 Chicago White Sox 978 1041 325 33 216 2000 Cleveland Indians 950 1078 310 30 221 2000 Detroit Tigers 823 1028 307 41 177 2000 Kansas City Royals 879 1186 281 27 150 2000 Minnesota Twins 748 1026 325 49 116 2000 New York Yankees 871 1017 294 25 205 2000 Oakland Athletics 947 958 281 23 239 2000 Seattle Mariners 907 957 300 26 198 2000 Tampa Bay Devil Rays 733 977 253 22 162 2000 Texas Rangers 848 1063 330 35 173 2000 Toronto Blue Jays 861 969 328 21 244 2000 Arizona Diamondbacks 792 961 282 44 179 2000 Atlanta Braves 810 1011 274 26 179 2000 Chicago Cubs 764 948 272 23 183 2000 Cincinnati Reds 825 1007 302 36 200 2000 Colorado Rockies 968 1130 320 53 161 2000 Florida Marlins 731 978 274 29 160 2000 Houston Astros 938 973 289 36 249 2000 Los Angeles Dodgers 798 904 265 28 211 2000 Milwaukee Brewers 740 867 297 25 177 2000 Montreal Expos 738 952 310 35 178 2000 New York Mets 807 945 282 20 198 2000 Philadelphia Phillies 708 898 304 40 144 2000 Pittsburgh Pirates 793 987 320 31 168 2000 San Diego Padres 752 940 279 37 157 2000 San Francisco Giants 925 961 304 44 226 2000 St. Louis Cardinals 887 962 259 25 235 2001 Anaheim Angels 691 988 275 26 158 2001 Baltimore Orioles 687 937 262 24 136 2001 Boston Red Sox 772 950 316 29 198 2001 Chicago White Sox 798 920 300 29 214 2001 Cleveland Indians 897 1016 294 37 212 2001 Detroit Tigers 724 949 291 60 139 2001 Kansas City Royals 729 1037 277 37 152 2001 Minnesota Twins 771 984 328 38 164 2001 New York Yankees 804 976 289 20 203 2001 Oakland Athletics 884 914 334 22 199 2001 Seattle Mariners 927 1120 310 38 169 2001 Tampa Bay Devil Rays 672 973 311 21 121 2001 Texas Rangers 890 971 326 23 246 2001 Toronto Blue Jays 767 971 287 36 195 2001 Arizona Diamondbacks 818 967 284 35 208 2001 Atlanta Braves 729 971 263 24 174 2001 Chicago Cubs 777 915 268 32 194 2001 Cincinnati Reds 735 962 304 22 176 2001 Colorado Rockies 923 1065 324 61 213 2001 Florida Marlins 742 940 325 30 166 2001 Houston Astros 847 950 313 29 208 2001 Los Angeles Dodgers 758 902 264 27 206 2001 Milwaukee Brewers 740 866 273 30 209 2001 Montreal Expos 670 882 320 28 131 2001 New York Mets 642 923 273 18 147 2001 Philadelphia Phillies 746 943 295 29 164 2001 Pittsburgh Pirates 657 891 256 25 161 2001 San Diego Padres 789 919 273 26 161 2001 San Francisco Giants 799 914 304 40 235 2001 St. Louis Cardinals 814 964 274 32 199 2002 St. Louis Cardinals 787 989 285 26 175 2002 Tampa Bay Devil Rays 673 953 297 35 133 2002 San Diego Padres 662 985 243 29 136 2002 Seattle Mariners 814 1063 285 31 152 2002 San Francisco Giants 783 932 300 35 198 2002 Anaheim Angels 851 1086 333 32 152 2002 Arizona Diamondbacks 819 982 283 41 165 2002 Atlanta Braves 708 959 280 25 164 2002 Baltimore Orioles 667 850 311 27 165 2002 Boston Red Sox 859 1002 348 33 177 2002 Chicago Cubs 706 863 259 29 200 2002 Chicago White Sox 856 940 289 29 217 2002 Cincinnati Reds 709 899 297 21 169 2002 Cleveland Indians 739 876 255 26 192 2002 Colorado Rockies 778 1032 283 41 152 2002 Detroit Tigers 575 914 265 37 124 2002 Florida Marlins 699 975 280 32 146 2002 Houston Astros 749 951 291 32 167 2002 Kansas City Royals 737 948 285 42 140 2002 Los Angeles Dodgers 713 994 286 29 155 2002 Milwaukee Brewers 627 932 269 29 139 2002 Minnesota Twins 768 967 348 36 167 2002 Montreal Expos 735 934 300 36 162 2002 New York Mets 690 989 238 22 160 2002 New York Yankees 897 991 314 12 223 2002 Oakland Athletics 800 938 279 28 205 2002 Philadelphia Phillies 710 897 325 41 165 2002 Pittsburgh Pirates 641 875 263 20 142 2002 Texas Rangers 843 949 304 27 230 2002 Toronto Blue Jays 813 927 305 38 187 2003 Anaheim Angels 736 1014 276 33 150 2003 Arizona Diamondbacks 717 965 303 47 152 2003 Atlanta Braves 907 1021 321 31 235 2003 Baltimore Orioles 743 1063 277 24 152 2003 Boston Red Sox 961 1018 371 40 238 2003 Chicago White Sox 791 903 303 19 220 2003 Chicago Cubs 724 933 302 24 172 2003 Cincinnati Reds 694 907 239 21 182 2003 Cleveland Indians 699 933 296 26 158 2003 Colorado Rockies 853 913 330 31 198 2003 Detroit Tigers 591 919 201 39 153 2003 Florida Marlins 751 966 292 44 157 2003 Houston Astros 805 937 308 30 191 2003 Kansas City Royals 836 1037 288 39 162 2003 Los Angeles Dodgers 574 919 260 25 124 2003 Milwaukee Brewers 714 937 266 24 196 2003 Minnesota Twins 801 1049 318 45 155 2003 Montreal Expos 711 941 294 25 144 2003 New York Yankees 877 970 304 14 230 2003 New York Mets 642 907 262 24 124 2003 Oakland Athletics 768 881 317 24 176 2003 Philadelphia Phillies 791 930 325 27 166 2003 Pittsburgh Pirates 753 1009 275 45 163 2003 San Diego Padres 678 1025 257 32 128 2003 Seattle Mariners 795 1047 290 33 139 2003 San Francisco Giants 755 950 281 29 180 2003 St. Louis Cardinals 876 1010 342 32 196 2003 Tampa Bay Devil Rays 715 1028 298 38 137 2003 Texas Rangers 826 957 274 36 239 2003 Toronto Blue Jays 894 1000 357 33 190 2004 Anaheim Angels 836 1132 272 37 162 2004 Arizona Diamondbacks 615 933 295 38 135 2004 Atlanta Braves 803 984 304 37 178 2004 Baltimore Orioles 842 1108 319 18 169 2004 Boston Red Sox 949 993 373 25 222 2004 Chicago White Sox 865 936 284 19 242 2004 Chicago Cubs 789 936 308 29 235 2004 Cincinnati Reds 750 871 287 28 194 2004 Cleveland Indians 858 1007 345 29 184 2004 Colorado Rockies 833 964 331 34 202 2004 Detroit Tigers 827 992 284 54 201 2004 Florida Marlins 718 992 275 32 148 2004 Houston Astros 803 941 294 36 187 2004 Kansas City Royals 720 992 261 29 150 2004 Los Angeles Dodgers 761 991 226 30 203 2004 Milwaukee Brewers 634 896 295 32 135 2004 Minnesota Twins 780 969 310 24 191 2004 Montreal Expos 635 907 276 27 151 2004 New York Yankees 897 940 281 20 242 2004 New York Mets 684 882 289 20 185 2004 Oakland Athletics 793 1005 336 15 189 2004 Philadelphia Phillies 840 964 303 23 215 2004 Pittsburgh Pirates 680 980 267 39 142 2004 San Diego Padres 768 1046 304 32 139 2004 Seattle Mariners 698 1112 276 20 136 2004 San Francisco Giants 850 970 314 33 183 2004 St. Louis Cardinals 855 987 319 24 214 2004 Tampa Bay Devil Rays 714 947 278 46 145 2004 Texas Rangers 860 908 323 34 227 2004 Toronto Blue Jays 719 969 290 34 145 2005 Chicago White Sox 741 974 253 23 200 2005 Cleveland Indians 790 948 337 30 207 2005 Minnesota Twins 688 1006 269 32 134 2005 Detroit Tigers 723 1025 283 45 168 2005 Kansas City Royals 701 996 289 34 126 2005 New York Yankees 886 1048 259 16 229 2005 Boston Red Sox 910 1020 339 21 199 2005 Toronto Blue Jays 775 998 307 39 136 2005 Baltimore Orioles 729 980 296 27 189 2005 Tampa Bay Devil Rays 750 1033 289 40 157 2005 Los Angeles Angels of Anaheim 761 1065 278 30 147 2005 Oakland Athletics 772 991 310 20 155 2005 Texas Rangers 865 928 311 29 260 2005 Seattle Mariners 699 955 289 34 130 2005 St. Louis Cardinals 805 1011 287 26 170 2005 Houston Astros 693 926 281 32 161 2005 Milwaukee Brewers 726 892 327 19 175 2005 Chicago Cubs 703 966 323 23 194 2005 Cincinnati Reds 820 881 335 15 222 2005 Pittsburgh Pirates 680 976 292 38 139 2005 Atlanta Braves 769 924 308 37 184 2005 Philadelphia Phillies 807 1010 282 35 167 2005 Florida Marlins 717 1033 306 32 128 2005 New York Mets 722 935 279 32 175 2005 Washington Nationals 639 907 311 32 117 2005 San Diego Padres 684 978 269 39 130 2005 Arizona Diamondbacks 696 910 291 27 191 2005 San Francisco Giants 649 974 299 26 128 2005 Los Angeles Dodgers 685 920 284 21 149 2005 Colorado Rockies 740 1013 280 34 150 2006 Arizona Diamondbacks 773 977 331 38 160 2006 Atlanta Braves 849 950 312 26 222 2006 Baltimore Orioles 768 1084 288 20 164 2006 Boston Red Sox 820 975 327 16 192 2006 Chicago White Sox 868 1039 291 20 236 2006 Chicago Cubs 716 1013 271 46 166 2006 Cincinnati Reds 749 899 291 12 217 2006 Cleveland Indians 870 1002 351 27 196 2006 Colorado Rockies 813 968 325 54 157 2006 Detroit Tigers 822 1011 294 40 203 2006 Florida Marlins 758 921 309 42 182 2006 Houston Astros 735 931 275 27 174 2006 Kansas City Royals 757 1019 335 37 124 2006 Los Angeles Angels of Anaheim 766 1042 309 29 159 2006 Los Angeles Dodgers 820 1034 307 58 153 2006 Milwaukee Brewers 730 899 301 20 180 2006 Minnesota Twins 801 1156 275 34 143 2006 New York Yankees 930 1050 327 21 210 2006 New York Mets 834 905 323 41 200 2006 Oakland Athletics 771 966 266 22 175 2006 Philadelphia Phillies 865 967 294 41 216 2006 Pittsburgh Pirates 691 1018 286 17 141 2006 San Diego Padres 731 968 298 38 161 2006 Seattle Mariners 756 1060 266 42 172 2006 San Francisco Giants 746 906 297 52 163 2006 St. Louis Cardinals 781 981 292 27 184 2006 Tampa Bay Devil Rays 689 905 267 33 190 2006 Texas Rangers 835 1008 357 23 183 2006 Toronto Blue Jays 809 1017 348 27 199 2006 Washington Nationals 746 929 322 22 164

Explanation / Answer

Provided data of runs from 2000 to 2006

We want to build Regression Model on 2000 to 2004 data and predict the value for 2005 and 2006

By using R-studio The regression model:

> Model = lm(Runs~ Single + Double + Triples + HR , data = data)

> Model

Coefficients:

(Intercept) Singles Double Triples HR  

-448.3694 0.6515 0.8058 0.8070 1.8678  

Then fitted model from above data is,

Runs = - 448.3694 + 0.6515 * Single +  0.8058 * Double + 0.8070 * Triple + 1.8678 * HR

> summary(Model)

Residuals summary:

Min 1Q Median 3Q Max

-83.009 -20.462 -0.753 20.564 99.287

Coefficients Estimate Std. Error t value Pr(>|t|)   

(Intercept) -448.36937 51.52590 -8.702 6.57e-15 ***

Singles 0.65153 0.04869 13.381 < 2e-16 ***

Double 0.80583 0.10784 7.473 6.81e-12 ***

Triples 0.80698 0.33781 2.389 0.0182 *  

HR 1.86784 0.08920 20.941 < 2e-16 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

All stared variable is significant that is an important factor that effect on response variable runs

also, p-value is less than 0.05 level of significance therefore all stared variable is significant

Residual standard error: 33.12 on 145 degrees of freedom

Multiple R-squared: 0.8541, Adjusted R-squared: 0.8501

Adjusted R-squared is more than 0.80 model is very good

F-statistic: 212.2 on 4 and 145 DF,

p-value: < 2.2e-16

The p-value of F-statistic is less than 0.05 so model is significant

# The Predicted value and Error term:

> Predicted_Runs = predict(Model,data)
> Error = data$Runs - Predicted_Runs
> data.frame(Predicted_Runs,Error)
Predicted_Runs Error
1 917.1581 -53.1581246
2 809.1977 -15.1976727
3 787.7430 4.2570467
4 921.8581 56.1418584
5 940.7957 9.2042955
6 832.4931 -9.4930829
7 852.7543 26.2456830
8 738.2123 9.7877120
9 854.2384 16.7616159
10 867.2148 79.7851850
11 807.7134 99.2866063
12 712.3996 20.6003938
13 861.5177 -13.5176798
14 919.9811 -58.9810958
15 774.8511 17.1488985
16 786.4555 23.5444661
17 748.8477 15.1523401
18 853.7072 -28.7072435
19 889.2236 78.7763831
20 731.8868 -0.8867873
21 912.6037 25.3963394
22 770.8739 27.1261202
23 706.6261 33.3739031
24 782.4200 -44.4199575
25 780.5481 26.4518766
26 682.9303 25.0697206
27 791.3756 1.6243836
28 712.0099 39.9900540
29 880.3681 44.6318648
30 846.2352 40.7647906
31 733.0513 -42.0513360
32 646.6407 40.3592787
33 818.4669 -46.4669135
34 815.9131 -17.9130848
35 876.3455 20.6544922
36 712.4830 11.5169562
37 764.2579 -35.2578704
38 794.0451 -23.0451457
39 815.7257 -11.7257366
40 805.7357 78.2643330
41 877.4880 49.5119707
42 679.1431 -7.1431436
43 925.0221 -35.0221459
44 808.8253 -41.8252978
45 827.2767 -9.2766692
46 740.5768 -11.5768252
47 751.9328 25.0671966
48 769.8739 -34.8738914
49 953.6810 -30.6809944
50 760.2400 -18.2400053
51 834.7279 12.2721348
52 758.6188 -0.6187752
53 750.4405 -10.4405101
54 651.4333 18.5666718
55 662.0878 -20.0878260
56 733.4770 12.5230419
57 659.3383 -2.3382563
58 692.0873 96.9126523
59 863.3287 -64.3287196
60 798.0322 15.9678010
61 773.5146 13.4854380
62 688.5426 -15.5426422
63 666.6384 -4.6384330
64 782.8025 31.1974510
65 798.6878 -15.6878466
66 837.2748 13.7252165
67 760.7684 58.2316137
68 728.5861 -20.5860999
69 686.0315 -19.0314912
70 842.1365 16.8634932
71 719.5867 -13.5866663
72 825.6831 30.3168566
73 709.3045 -0.3045162
74 707.4696 31.5304159
75 769.0631 8.9368899
76 622.1495 -47.1495152
77 711.0383 -12.0382870
78 743.4904 5.5096287
79 694.3387 42.6612562
80 742.6421 -29.6421016
81 658.6623 -31.6623072
82 803.0753 -35.0752967
83 733.5555 1.4445258
84 704.3948 -14.3948357
85 876.5456 20.4543622
86 793.1006 6.8993704
87 739.2330 -29.2329553
88 615.0306 25.9694091
89 866.3025 -23.3024692
90 781.3340 31.6660198
91 741.5031 -5.5031474
92 746.3688 -29.3688462
93 939.4792 -32.4792248
94 770.7070 -27.7070373
95 990.6826 -29.6825998
96 810.3918 -19.3917861
97 743.5103 -19.5103122
98 692.0605 1.9395227
99 714.1394 -15.1394434
100 807.2558 45.7442358
101 629.6154 -38.6153545
102 745.0745 5.9254902
103 791.2824 13.7176287
104 793.4144 42.5855629
105 611.6943 -37.6942796
106 761.9348 -47.9347511
107 817.1748 -16.1747850
108 690.7832 20.2167570
109 869.4940 7.5060348
110 604.6806 37.3194437
111 729.1894 38.8105942
112 751.3037 39.6962722
113 771.4054 -18.4053716
114 691.4596 -13.4596337
115 753.7391 41.2608618
116 756.6416 -1.6415591
117 877.1959 -1.1958600
118 748.1059 -33.1058535
119 871.4132 -45.4131734
120 872.3679 21.6320824
121 840.8029 -4.8029030
122 680.0569 -65.0569191
123 800.0480 2.9519881
124 860.7825 -18.7825419
125 934.0157 14.9842875
126 857.6742 7.3258181
127 872.0090 -83.0090378
128 735.3482 14.6517931
129 852.8237 5.1763199
130 851.1822 -18.1821554
131 845.8227 -18.8227017
132 721.8209 -3.8208944
133 779.9773 23.0226583
134 711.8540 8.1460093
135 782.8011 -21.8010745
136 651.1083 -17.1082832
137 808.9013 -28.9012588
138 668.8150 -33.8149645
139 858.6698 38.3302009
140 720.8603 -36.8603147
141 842.3096 -49.3096421
142 844.0241 -4.0240600
143 701.9976 -21.9976028
144 763.5623 4.4377167
145 768.7129 -70.7129449
146 805.0962 44.9038289
147 870.8418 -15.8418028
148 700.6135 13.3864800
149 854.9457 5.0542953
150 714.9335 4.0664788
151 782.2301 -41.2300916
152 851.7039 -61.7039155
153 699.9575 -11.9575468
154 797.6158 -74.6158049
155 696.2301 4.7699435
156 883.7973 2.2027290
157 878.0205 31.9795259
158 734.7515 40.2485437
159 803.4717 -74.4717225
160 783.0819 -33.0818868
161 768.3186 -7.3185849
162 752.7647 19.2353232
163 915.9104 -50.9103872
164 676.9885 22.0114646
165 780.1208 24.8792457
166 707.9366 -14.9366201
167 738.5119 -12.5118709
168 822.2190 -119.2190378
169 822.3525 -2.3524565
170 713.1268 -33.1267703
171 775.3864 -6.3863623
172 777.0993 29.9006712
173 736.1577 -19.1577097
174 738.3386 -16.3385919
175 637.5473 1.4527273
176 679.8921 4.1079399
177 757.5709 -61.5708569
178 687.2345 -38.2344931
179 675.1540 9.8459911
180 744.8819 -4.8819227
181 784.4305 -11.4305247
182 857.6509 -8.6509265
183 812.4396 -44.4396401
184 821.9216 -1.9216361
185 920.0229 -52.0229393
186 777.1987 -61.1986910
187 786.8633 -37.8632719
188 875.2012 -5.2011881
189 781.0398 31.9601567
190 858.6982 -36.6981678
191 774.5368 -16.5367954
192 726.6064 8.3936135
193 746.9689 10.0311073
194 799.9213 -33.9212741
195 805.2926 14.7073557
196 732.2672 -2.2671632
197 820.9472 -19.9472308
198 908.4428 21.5571984
199 808.2081 25.7918623
200 739.9905 31.0094597
201 855.1196 9.8803724
202 722.4453 -31.4453490
203 753.8421 -22.8420828
204 811.7708 -55.7707891
205 727.6745 18.3254785
206 791.5607 -10.5607010
207 737.9472 -48.9472276
208 856.4355 -21.4354902
209 888.1602 -79.1602375
210 740.4641 5.5358873

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