# ISDS 361B Regression, Exercises for Business Statistics

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Assignment Miles (X) Time (Y) Y_hat residual squarred error 1 100 9.3 8.0539 1.2461 1.55276521 2 50 4.8 4.6639 0.1361 0.01852321 3 100 8.9 8.0539 0.8461 0.71588521 4 100 6.5 8.0539 -1.5539 2.41460521 5 50 4.2 4.6639 -0.4639 0.21520321 6 80 6.2 6.6979 -0.4979 0.24790441 7 75 7.4 6.3589 1.0411 1.08388921 8 65 6.0 5.6809 0.3191 0.10182481 9 90 7.6 7.3759 0.2241 0.05022081

10 90 6.1 7.3759 -1.2759 1.62792081 B0= 1.2739 8.0287421 B1= 0.0678 "=sum of square error"

40 50 60 70 80 90 100 110 0

1

2

3

4

5

6

7

8

9

10

f(x) = 0.067826086956522 x + 1.27391304347826 R² = 0.664071311624523

Time (Y)

the sum of squares SSE unexplained variance =sum(y1-y_hat)

total sum of squares SST total variation =sum(y1-Y_bar) S^2y= SST n-1

SSR= SST-SSE this is the explained variance =sum (y_hat- y_bar)^2

R squared is the proportion of variance that is explained by the linear relationship.

therefore SSR , = 1- SSE SST SST

the regression analysis you make sure to calculate for the residuals (a check box)

(y-y_bar) (y-y_bar)^2 2.6 6.76 -1.9 3.61 R^2 2.2 4.84 0.664069 "=1-SSE/SST" -0.2 0.04 0.664071 "=correl(array y, arrayX)^2" -2.5 6.25 -0.5 0.25 0.7 0.49 -0.7 0.49 0.9 0.809999999999999 -0.6 0.360000000000001

23.9 ^sum of squares total^

40 50 60 70 80 90 100 110 0

1

2

3

4

5

6

7

8

9

10

f(x) = 0.067826086956522 x + 1.27391304347826 R² = 0.664071311624523

Time (Y)

the sum of squares SSE unexplained variance =sum(y1-y_hat)

total sum of squares SST total variation =sum(y1-Y_bar) S^2y= SST n-1

SSR= SST-SSE this is the explained variance =sum (y_hat- y_bar)^2

R squared is the proportion of variance that is explained by the linear relationship.

therefore SSR , = 1- SSE SST SST

the regression analysis you make sure to calculate for the residuals (a check box)

SUMMARY OUTPUT

Regression Statistics Multiple R 0.8149057072 R Square 0.6640713116 Adjusted R Squa 0.6220802256 Standard Error 1.0017918729 Observations 10

ANOVA df SS MS F

Reduced,Explained Regression 1 15.8713043478 15.87130434783 15.81458 Not Explained/ error Residual 8 8.02869565217 1.003586956522

Total 9 23.9

Coefficients Standard Error t Stat P-value Intercept 1.2739130435 1.40074452478 0.909454237332 0.389687 Miles 0.067826087 0.01705563748 3.976754725101 0.00408

RESIDUAL OUTPUT

Observation Predicted Time Residuals Squared Error Data 1 8.0565217391 1.24347826087 1.546238185255 - 2 4.6652173913 0.1347826087 0.018166351607 - 3 8.0565217391 0.84347826087 0.71145557656 - 4 8.0565217391 -1.5565217391 2.422759924386 5 4.6652173913 -0.4652173913 0.216427221172 6 6.7 -0.5 0.25 7 6.3608695652 1.03913043478 1.079792060492 8 5.6826086957 0.31739130435 0.100737240076 9 7.3782608696 0.22173913043 0.049168241966

10 7.3782608696 -1.2782608696 1.633950850662 8.028695652174

Significance F 0.00408

Lower 95%Upper 95%Lower 95.0%Upper 95.0% -1.95621 4.504036 -1.95621 4.504036 0.028496 0.107156 0.028496 0.107156

Data analysis regression residual check box

40 50 60 70 80 90 100 110 0 2 4 6 8

10

Miles Line Fit Plot

Time Predicted Time

Miles

Ti m

e

40 50 60 70 80 90 100 110 0 2 4 6 8

10

Miles Line Fit Plot

Time Predicted Time

Miles

Ti m

e

Assignment Miles (X1) Deliveries (X2)Time (Y) Predicted Time (Y_Hat) 1 100.0 4.0 9.3 9.60550446374317 2 50.0 3.0 4.8 5.55641908065995 3 100.0 4.0 8.9 9.60550446374317 4 100.0 2.0 6.5 8.22550790293472 5 50.0 2.0 4.2 4.86642080025573 6 80.0 2.0 6.2 6.88187306186313 7 75.0 3.0 7.4 7.23596263199945 8 65.0 4.0 6.0 7.25414349186788 9 90.0 3.0 7.6 8.24368876280315

10 90.0 2.0 6.1 7.55369048239892 11 50.0 5.0 7.0 6.9364156414684 12 45.0 6.0 7.0 7.29050521160473 13 85.0 5.0 9.6 9.2877766133437 14 65.0 2.0 6.5 5.87414693105943 15 40.0 6.0 7.2 6.95459650133683 16 50.0 3.0 6.0 5.55641908065995 17 75.0 5.0 9.9 8.6159591928079 18 75.0 4.0 8.6 7.92596091240367 19 65.0 3.0 4.9 6.56414521146365 20 90.0 3.0 7.5 8.24368876280315 21 95.0 1.0 7.2 7.1996009122626 22 95.0 6.0 9.9 10.6495923142837 23 50.0 1.0 5.6 4.17642251985151 24 80.0 3.0 7.5 7.57187134226735 25 90.0 2.0 7.8 7.55369048239892 26 80.0 3.0 7.2 7.57187134226735 27 75.0 3.0 7.0 7.23596263199945 28 95.0 2.0 8.7 7.88959919266682 29 90.0 1.0 6.4 6.8636922019947 30 100.0 3.0 9.9 8.91550618333894 31 60.0 1.0 4.1 4.8482399403873 32 90.0 4.0 9.3 8.93368704320737 33 70.0 5.0 9.1 8.28005048254 34 100.0 5.0 8.9 10.2955027441474 35 40.0 4.0 5.4 5.57459994052838 36 80.0 2.0 5.9 6.88187306186313 37 90.0 4.0 8.8 8.93368704320737 38 80.0 5.0 8.4 8.9518679030758 39 95.0 2.0 9.4 7.88959919266682 40 75.0 5.0 8.8 8.6159591928079 41 40.0 3.0 5.0 4.88460166012415 42 45.0 3.0 6.5 5.22051037039205 43 75.0 6.0 8.7 9.30595747321212 44 95.0 4.0 8.4 9.26959575347527 45 55.0 2.0 7.1 5.20232951052363

46 75.0 3.0 6.1 7.23596263199945 47 55.0 2.0 5.2 5.20232951052363 48 100.0 6.0 10.0 10.9855010245516 49 50.0 4.0 5.1 6.24641736106418 50 40.0 1.0 3.6 3.50460509931571 51 90.0 4.0 8.4 8.93368704320737 52 80.0 1.0 6.4 6.1918747814589 53 80.0 3.0 6.7 7.57187134226735 54 90.0 5.0 8.5 9.6236853236116 55 60.0 4.0 5.9 6.91823478159998 56 40.0 2.0 2.8 4.19460337971993 57 70.0 4.0 7.9 7.59005220213577 58 95.0 3.0 8.9 8.57959747307105 59 40.0 5.0 6.0 6.2645982209326 60 45.0 1.0 3.1 3.84051380958361 61 45.0 5.0 6.3 6.6005069312005 62 65.0 5.0 7.5 7.9441417722721 63 85.0 2.0 7.2 7.21778177213102 64 85.0 2.0 8.0 7.21778177213102 65 75.0 3.0 6.8 7.23596263199945 66 45.0 4.0 5.1 5.91050865079628 67 40.0 1.0 3.2 3.50460509931571 68 90.0 1.0 5.9 6.8636922019947 69 100.0 2.0 7.8 8.22550790293472 70 75.0 1.0 5.8 5.855966071191 71 45.0 1.0 3.8 3.84051380958361 72 85.0 1.0 6.8 6.5277834917268 73 60.0 2.0 5.7 5.53823822079153 74 70.0 2.0 5.5 6.21005564132733 75 85.0 4.0 9.2 8.59777833293947 76 70.0 5.0 9.0 8.28005048254 77 85.0 6.0 9.3 9.97777489374792 78 85.0 5.0 8.8 9.2877766133437 79 40.0 5.0 7.1 6.2645982209326 80 95.0 5.0 10.8 9.95959403387949 81 45.0 5.0 6.9 6.6005069312005 82 85.0 6.0 9.4 9.97777489374792 83 45.0 2.0 3.6 4.53051208998783 84 95.0 1.0 7.6 7.1996009122626 85 65.0 5.0 8.5 7.9441417722721 86 85.0 3.0 7.1 7.90778005253525 87 40.0 6.0 7.1 6.95459650133683 88 55.0 3.0 6.0 5.89232779092785 89 45.0 2.0 5.3 4.53051208998783 90 65.0 3.0 6.3 6.56414521146365 91 85.0 5.0 10.2 9.2877766133437

92 75.0 2.0 7.6 6.54596435159523 93 40.0 3.0 6.0 4.88460166012415 94 85.0 4.0 8.9 8.59777833293947 95 85.0 1.0 7.6 6.5277834917268 96 40.0 6.0 6.6 6.95459650133683 97 55.0 6.0 8.0 7.96232263214052 98 90.0 6.0 9.7 10.3136836040158 99 85.0 1.0 6.2 6.5277834917268

100 45.0 1.0 4.3 3.84051380958361 101 50.0 2.0 4.2 4.86642080025573 102 60.0 4.0 8.0 6.91823478159998 103 45.0 2.0 5.5 4.53051208998783 104 85.0 4.0 8.9 8.59777833293947 105 90.0 1.0 7.1 6.8636922019947 106 40.0 2.0 5.5 4.19460337971993 107 80.0 4.0 9.3 8.26186962267157 108 70.0 4.0 9.2 7.59005220213577 109 70.0 2.0 6.3 6.21005564132733 110 80.0 4.0 8.6 8.26186962267157 111 100.0 6.0 11.0 10.9855010245516 112 75.0 1.0 6.7 5.855966071191 113 50.0 3.0 5.5 5.55641908065995 114 45.0 6.0 8.1 7.29050521160473 115 100.0 6.0 10.2 10.9855010245516 116 100.0 2.0 7.7 8.22550790293472 117 80.0 4.0 7.2 8.26186962267157 118 100.0 3.0 9.0 8.91550618333894 119 100.0 6.0 10.4 10.9855010245516 120 45.0 3.0 5.1 5.22051037039205 121 50.0 4.0 6.4 6.24641736106418 122 40.0 4.0 4.1 5.57459994052838 123 100.0 3.0 8.0 8.91550618333894 124 95.0 4.0 8.5 9.26959575347527 125 50.0 2.0 3.6 4.86642080025573 126 65.0 4.0 7.3 7.25414349186788 127 50.0 6.0 6.9 7.62641392187262 128 85.0 4.0 8.7 8.59777833293947 129 90.0 3.0 8.8 8.24368876280315 130 45.0 5.0 8.3 6.6005069312005 131 50.0 6.0 9.3 7.62641392187262 132 55.0 5.0 7.5 7.2723243517363 133 45.0 3.0 5.7 5.22051037039205 134 95.0 4.0 8.5 9.26959575347527 135 60.0 6.0 7.4 8.29823134240842 136 55.0 1.0 5.9 4.5123312301194 137 85.0 1.0 8.0 6.5277834917268

138 95.0 3.0 8.7 8.57959747307105 139 55.0 3.0 6.1 5.89232779092785 140 50.0 4.0 7.1 6.24641736106418 141 45.0 6.0 6.3 7.29050521160473 142 50.0 3.0 5.2 5.55641908065995 143 50.0 5.0 6.0 6.9364156414684 144 90.0 3.0 8.4 8.24368876280315 145 65.0 4.0 7.2 7.25414349186788 146 60.0 6.0 7.9 8.29823134240842 147 40.0 5.0 5.2 6.2645982209326 148 80.0 3.0 7.0 7.57187134226735 149 100.0 1.0 6.9 7.5355096225305 150 70.0 6.0 10.6 8.97004876294422 151 90.0 5.0 9.0 9.6236853236116 152 70.0 3.0 5.6 6.90005392173155 153 100.0 3.0 8.8 8.91550618333894 154 85.0 4.0 9.1 8.59777833293947 155 90.0 6.0 11.2 10.3136836040158 156 40.0 4.0 4.2 5.57459994052838 157 85.0 2.0 6.3 7.21778177213102 158 50.0 1.0 3.5 4.17642251985151 159 40.0 5.0 7.2 6.2645982209326 160 60.0 1.0 4.8 4.8482399403873 161 85.0 5.0 7.9 9.2877766133437 162 80.0 2.0 5.7 6.88187306186313 163 45.0 5.0 6.2 6.6005069312005 164 100.0 1.0 7.0 7.5355096225305 165 100.0 6.0 12.2 10.9855010245516 166 55.0 1.0 3.5 4.5123312301194 167 70.0 2.0 5.7 6.21005564132733 168 100.0 4.0 10.0 9.60550446374317 169 75.0 2.0 6.3 6.54596435159523 170 40.0 5.0 6.5 6.2645982209326 171 80.0 1.0 7.4 6.1918747814589 172 90.0 2.0 6.8 7.55369048239892 173 75.0 2.0 5.4 6.54596435159523 174 40.0 1.0 3.5 3.50460509931571 175 50.0 4.0 6.5 6.24641736106418 176 85.0 3.0 9.4 7.90778005253525 177 45.0 3.0 4.6 5.22051037039205 178 60.0 5.0 8.3 7.6082330620042 179 80.0 4.0 8.5 8.26186962267157 180 55.0 4.0 5.8 6.58232607133208 181 55.0 5.0 6.7 7.2723243517363 182 90.0 6.0 8.9 10.3136836040158 183 40.0 4.0 5.0 5.57459994052838

184 80.0 2.0 7.3 6.88187306186313 185 40.0 5.0 5.9 6.2645982209326 186 60.0 2.0 6.0 5.53823822079153 187 90.0 5.0 9.9 9.6236853236116 188 55.0 2.0 5.7 5.20232951052363 189 75.0 3.0 5.7 7.23596263199945 190 55.0 4.0 6.8 6.58232607133208 191 65.0 3.0 7.6 6.56414521146365 192 45.0 4.0 5.0 5.91050865079628 193 85.0 5.0 11.1 9.2877766133437 194 85.0 3.0 7.7 7.90778005253525 195 65.0 6.0 8.5 8.63414005267632 196 100.0 2.0 10.0 8.22550790293472 197 40.0 5.0 6.1 6.2645982209326 198 55.0 5.0 7.0 7.2723243517363 199 90.0 6.0 10.1 10.3136836040158 200 50.0 3.0 4.6 5.55641908065995 201 65.0 2.0 5.5 5.87414693105943 202 80.0 1.0 6.3 6.1918747814589 203 70.0 1.0 6.2 5.5200573609231 204 70.0 5.0 8.5 8.28005048254 205 95.0 6.0 11.5 10.6495923142837 206 50.0 6.0 9.4 7.62641392187262 207 90.0 3.0 8.5 8.24368876280315 208 60.0 3.0 6.1 6.22823650119575 209 80.0 1.0 5.3 6.1918747814589 210 95.0 6.0 11.0 10.6495923142837 211 85.0 3.0 8.4 7.90778005253525 212 60.0 3.0 6.2 6.22823650119575 213 45.0 5.0 5.0 6.6005069312005 214 85.0 2.0 5.7 7.21778177213102 215 85.0 3.0 6.8 7.90778005253525 216 50.0 4.0 4.5 6.24641736106418 217 85.0 5.0 8.9 9.2877766133437 218 75.0 2.0 5.9 6.54596435159523 219 65.0 6.0 7.1 8.63414005267632 220 40.0 3.0 3.1 4.88460166012415 221 95.0 6.0 9.7 10.6495923142837 222 90.0 3.0 9.6 8.24368876280315 223 95.0 4.0 9.8 9.26959575347527 224 55.0 2.0 5.5 5.20232951052363 225 40.0 4.0 6.4 5.57459994052838 226 70.0 5.0 7.7 8.28005048254 227 50.0 5.0 6.1 6.9364156414684 228 45.0 2.0 4.8 4.53051208998783 229 65.0 2.0 6.5 5.87414693105943

230 65.0 1.0 5.7 5.1841486506552 231 75.0 2.0 5.3 6.54596435159523 232 100.0 6.0 10.6 10.9855010245516 233 85.0 6.0 9.2 9.97777489374792 234 95.0 3.0 9.0 8.57959747307105 235 75.0 4.0 9.1 7.92596091240367 236 60.0 1.0 5.2 4.8482399403873 237 85.0 2.0 7.9 7.21778177213102 238 95.0 3.0 9.9 8.57959747307105 239 45.0 4.0 5.7 5.91050865079628 240 45.0 2.0 3.9 4.53051208998783 241 90.0 6.0 9.1 10.3136836040158 242 60.0 5.0 8.3 7.6082330620042 243 60.0 5.0 7.2 7.6082330620042 244 80.0 4.0 8.5 8.26186962267157 245 45.0 3.0 5.6 5.22051037039205 246 100.0 5.0 11.7 10.2955027441474 247 45.0 3.0 4.9 5.22051037039205 248 55.0 3.0 6.4 5.89232779092785 249 65.0 2.0 6.8 5.87414693105943 250 70.0 6.0 10.3 8.97004876294422 251 55.0 5.0 8.8 7.2723243517363 252 90.0 3.0 8.8 8.24368876280315 253 100.0 4.0 9.5 9.60550446374317 254 75.0 4.0 8.7 7.92596091240367 255 75.0 5.0 8.9 8.6159591928079 256 65.0 6.0 7.5 8.63414005267632 257 75.0 2.0 5.8 6.54596435159523 258 75.0 4.0 8.2 7.92596091240367 259 55.0 2.0 5.8 5.20232951052363 260 60.0 5.0 8.0 7.6082330620042 261 95.0 3.0 9.0 8.57959747307105 262 85.0 2.0 7.4 7.21778177213102 263 70.0 4.0 7.0 7.59005220213577 264 100.0 5.0 10.3 10.2955027441474 265 100.0 4.0 9.2 9.60550446374317 266 90.0 4.0 8.5 8.93368704320737 267 70.0 6.0 8.9 8.97004876294422 268 95.0 6.0 12.3 10.6495923142837 269 40.0 3.0 5.7 4.88460166012415 270 100.0 2.0 9.4 8.22550790293472 271 60.0 1.0 4.0 4.8482399403873 272 40.0 5.0 7.9 6.2645982209326 273 60.0 1.0 5.7 4.8482399403873 274 100.0 6.0 11.2 10.9855010245516 275 95.0 6.0 11.3 10.6495923142837

276 55.0 1.0 3.4 4.5123312301194 277 50.0 2.0 4.5 4.86642080025573 278 90.0 3.0 8.4 8.24368876280315 279 65.0 4.0 8.8 7.25414349186788 280 45.0 1.0 3.7 3.84051380958361 281 45.0 1.0 4.7 3.84051380958361 282 80.0 5.0 8.3 8.9518679030758 283 80.0 1.0 7.1 6.1918747814589 284 85.0 6.0 11.3 9.97777489374792 285 65.0 3.0 6.1 6.56414521146365 286 90.0 1.0 8.0 6.8636922019947 287 65.0 3.0 7.3 6.56414521146365 288 90.0 2.0 7.2 7.55369048239892 289 40.0 5.0 7.6 6.2645982209326 290 85.0 2.0 7.8 7.21778177213102 291 75.0 2.0 6.5 6.54596435159523 292 70.0 2.0 6.1 6.21005564132733 293 75.0 4.0 7.2 7.92596091240367 294 70.0 6.0 8.9 8.97004876294422 295 95.0 6.0 10.9 10.6495923142837 296 50.0 4.0 7.2 6.24641736106418 297 50.0 1.0 3.5 4.17642251985151 298 85.0 2.0 8.0 7.21778177213102 299 100.0 2.0 7.8 8.22550790293472 300 65.0 6.0 10.0 8.63414005267632

Residuals with formula CompareResiduals -0.305504463743169 -0.305504463743169 -0.756419080659954 -0.756419080659953

-0.70550446374317 -0.70550446374317 -1.72550790293472 -1.72550790293472

-0.666420800255729 -0.666420800255729 -0.681873061863125 -0.681873061863125 0.164037368000551 0.164037368000551 -1.25414349186788 -1.25414349186788

-0.643688762803148 -0.643688762803148 -1.45369048239892 -1.45369048239892

0.0635843585316 0.0635843585316 -0.290505211604725 -0.290505211604725 0.312223386656305 0.312223386656305 0.625853068940573 0.625853068940573 0.245403498663174 0.245403498663174 0.443580919340047 0.443580919340047

1.2840408071921 1.2840408071921 0.674039087596327 0.674039087596327 -1.66414521146365 -1.66414521146365

-0.743688762803147 -0.743688762803147 0.000399087737402 0.000399087737402

-0.749592314283717 -0.749592314283717 1.42357748014849 1.42357748014849

-0.071871342267349 -0.071871342267349 0.246309517601076 0.246309517601076

-0.371871342267348 -0.371871342267348 -0.235962631999449 -0.235962631999449 0.810400807333177 0.810400807333177

-0.463692201994699 -0.463692201994699 0.984493816661056 0.984493816661056

-0.748239940387304 -0.748239940387304 0.36631295679263 0.36631295679263

0.819949517460001 0.819949517460001 -1.39550274414739 -1.39550274414739

-0.174599940528378 -0.174599940528378 -0.981873061863125 -0.981873061863125

-0.13368704320737 -0.13368704320737 -0.551867903075797 -0.551867903075797

1.51040080733318 1.51040080733318 0.184040807192105 0.184040807192105 0.115398339875846 0.115398339875846

1.27948962960795 1.27948962960795 -0.605957473212122 -0.605957473212122

-0.86959575347527 -0.86959575347527 1.89767048947637 1.89767048947637

The predicted time table was copied from the regression residual table that was conducted in the Mult. regression output.

*note how the residuals should be the same based on calculation and the actual value.

-1.13596263199945 -1.13596263199945 -0.002329510523628 -0.002329510523628 -0.985501024551617 -0.985501024551617

-1.14641736106418 -1.14641736106418 0.095394900684293 0.095394900684293

-0.533687043207371 -0.533687043207371 0.2081252185411 0.2081252185411

-0.871871342267348 -0.871871342267348 -1.1236853236116 -1.1236853236116

-1.01823478159998 -1.01823478159998 -1.39460337971993 -1.39460337971993 0.309947797864227 0.309947797864227 0.320402526928953 0.320402526928953

-0.264598220932602 -0.264598220932602 -0.740513809583606 -0.740513809583606 -0.300506931200502 -0.300506931200502 -0.444141772272099 -0.444141772272099 -0.017781772131024 -0.017781772131024 0.782218227868976 0.782218227868976

-0.435962631999449 -0.435962631999449 -0.810508650796278 -0.810508650796278 -0.304605099315707 -0.304605099315707 -0.963692201994699 -0.963692201994699 -0.425507902934721 -0.425507902934721 -0.055966071191001 -0.055966071191001 -0.040513809583607 -0.040513809583607

0.2722165082732 0.2722165082732 0.161761779208472 0.161761779208472

-0.710055641327326 -0.710055641327326 0.602221667060528 0.602221667060528 0.719949517460002 0.719949517460002 -0.67777489374792 -0.67777489374792

-0.487776613343694 -0.487776613343694 0.835401779067397 0.835401779067397 0.840405966120507 0.840405966120507 0.299493068799499 0.299493068799499 -0.57777489374792 -0.57777489374792 -0.93051208998783 -0.93051208998783 0.400399087737402 0.400399087737402 0.555858227727901 0.555858227727901

-0.807780052535248 -0.807780052535248 0.145403498663174 0.145403498663174 0.107672209072148 0.107672209072148 0.769487910012169 0.76948791001217

-0.264145211463651 -0.264145211463651 0.912223386656304 0.912223386656304

1.05403564840477 1.05403564840477 1.11539833987585 1.11539833987585

0.302221667060529 0.302221667060529 1.0722165082732 1.0722165082732

-0.354596501336826 -0.354596501336826 0.037677367859477 0.037677367859477

-0.613683604015819 -0.613683604015819 -0.3277834917268 -0.3277834917268

0.459486190416393 0.459486190416393 -0.666420800255729 -0.666420800255729

1.08176521840002 1.08176521840002 0.96948791001217 0.96948791001217

0.302221667060529 0.302221667060529 0.2363077980053 0.2363077980053

1.30539662028007 1.30539662028007 1.03813037732843 1.03813037732843 1.60994779786423 1.60994779786423

0.089944358672674 0.089944358672674 0.338130377328428 0.338130377328428 0.014498975448383 0.014498975448383 0.844033928808999 0.844033928808999

-0.056419080659953 -0.056419080659953 0.809494788395274 0.809494788395274

-0.785501024551618 -0.785501024551618 -0.525507902934721 -0.525507902934721

-1.06186962267157 -1.06186962267157 0.084493816661055 0.084493816661055

-0.585501024551617 -0.585501024551617 -0.120510370392054 -0.120510370392054 0.153582638935823 0.153582638935824 -1.47459994052838 -1.47459994052838

-0.915506183338945 -0.915506183338945 -0.76959575347527 -0.76959575347527 -1.26642080025573 -1.26642080025573 0.045856508132125 0.045856508132125

-0.726413921872624 -0.726413921872624 0.102221667060528 0.102221667060528 0.556311237196853 0.556311237196853

1.6994930687995 1.6994930687995 1.67358607812738 1.67358607812738

0.2276756482637 0.2276756482637 0.479489629607946 0.479489629607946 -0.76959575347527 -0.76959575347527

-0.898231342408423 -0.898231342408423 1.3876687698806 1.3876687698806 1.4722165082732 1.4722165082732

0.120402526928952 0.120402526928952 0.207672209072148 0.207672209072148 0.853582638935823 0.853582638935823

-0.990505211604726 -0.990505211604726 -0.356419080659953 -0.356419080659953

-0.9364156414684 -0.9364156414684 0.156311237196853 0.156311237196853

-0.054143491867875 -0.054143491867875 -0.398231342408423 -0.398231342408423

-1.0645982209326 -1.0645982209326 -0.571871342267349 -0.571871342267349 -0.635509622530497 -0.635509622530497

1.62995123705578 1.62995123705578 -0.623685323611596 -0.623685323611596

-1.30005392173155 -1.30005392173155 -0.115506183338944 -0.115506183338944 0.502221667060528 0.502221667060528 0.886316395984181 0.886316395984181 -1.37459994052838 -1.37459994052838

-0.917781772131025 -0.917781772131025 -0.676422519851506 -0.676422519851506 0.935401779067398 0.935401779067398

-0.048239940387304 -0.048239940387304 -1.38777661334369 -1.38777661334369 -1.18187306186312 -1.18187306186312

-0.400506931200502 -0.400506931200502 -0.535509622530498 -0.535509622530498

1.21449897544838 1.21449897544838 -1.0123312301194 -1.0123312301194

-0.510055641327326 -0.510055641327326 0.39449553625683 0.39449553625683

-0.245964351595226 -0.245964351595226 0.235401779067398 0.235401779067398

1.2081252185411 1.2081252185411 -0.753690482398924 -0.753690482398924

-1.14596435159523 -1.14596435159523 -0.004605099315707 -0.004605099315707 0.253582638935823 0.253582638935823

1.49221994746475 1.49221994746475 -0.620510370392054 -0.620510370392054 0.691766937995801 0.691766937995801 0.238130377328428 0.238130377328428

-0.782326071332077 -0.782326071332077 -0.5723243517363 -0.5723243517363

-1.41368360401582 -1.41368360401582 -0.574599940528378 -0.574599940528378

0.418126938136875 0.418126938136875 -0.364598220932602 -0.364598220932602 0.461761779208472 0.461761779208472 0.276314676388404 0.276314676388404 0.497670489476372 0.497670489476372 -1.53596263199945 -1.53596263199945 0.217673928667923 0.217673928667923

1.03585478853635 1.03585478853635 -0.910508650796277 -0.910508650796277

1.8122233866563 1.8122233866563 -0.207780052535248 -0.207780052535248 -0.134140052676322 -0.134140052676322

1.77449209706528 1.77449209706528 -0.164598220932603 -0.164598220932603

-0.2723243517363 -0.2723243517363 -0.213683604015818 -0.213683604015818 -0.956419080659954 -0.956419080659954 -0.374146931059427 -0.374146931059427 0.108125218541099 0.108125218541099 0.679942639076899 0.679942639076899 0.219949517460002 0.219949517460002 0.850407685716283 0.850407685716283

1.77358607812738 1.77358607812738 0.256311237196853 0.256311237196853

-0.128236501195752 -0.128236501195752 -0.891874781458901 -0.891874781458901 0.350407685716283 0.350407685716283 0.492219947464752 0.492219947464752

-0.028236501195751 -0.028236501195751 -1.6005069312005 -1.6005069312005

-1.51778177213102 -1.51778177213102 -1.10778005253525 -1.10778005253525 -1.74641736106418 -1.74641736106418

-0.387776613343695 -0.387776613343695 -0.645964351595225 -0.645964351595225

-1.53414005267632 -1.53414005267632 -1.78460166012415 -1.78460166012415

-0.949592314283718 -0.949592314283718 1.35631123719685 1.35631123719685 0.53040424652473 0.53040424652473

0.297670489476372 0.297670489476372 0.825400059471622 0.825400059471622

-0.580050482539998 -0.580050482539998 -0.836415641468401 -0.836415641468401 0.269487910012169 0.269487910012169 0.625853068940573 0.625853068940573

0.515851349344797 0.515851349344797 -1.24596435159523 -1.24596435159523

-0.385501024551617 -0.385501024551617 -0.777774893747921 -0.777774893747921 0.420402526928953 0.420402526928953

1.17403908759633 1.17403908759633 0.351760059612697 0.351760059612697 0.682218227868976 0.682218227868976

1.32040252692895 1.32040252692895 -0.210508650796277 -0.210508650796277 -0.630512089987831 -0.630512089987831

-1.21368360401582 -1.21368360401582 0.691766937995801 0.691766937995801

-0.408233062004199 -0.408233062004199 0.238130377328428 0.238130377328428 0.379489629607946 0.379489629607946

1.40449725585261 1.40449725585261 -0.320510370392054 -0.320510370392054 0.507672209072148 0.507672209072148 0.925853068940572 0.925853068940572

1.32995123705578 1.32995123705578 1.5276756482637 1.5276756482637

0.556311237196853 0.556311237196853 -0.10550446374317 -0.10550446374317 0.774039087596327 0.774039087596327 0.284040807192104 0.284040807192104 -1.13414005267632 -1.13414005267632

-0.745964351595226 -0.745964351595226 0.274039087596327 0.274039087596327 0.597670489476371 0.597670489476371 0.391766937995801 0.391766937995801 0.420402526928953 0.420402526928953 0.182218227868976 0.182218227868976

-0.590052202135773 -0.590052202135773 0.004497255852607 0.004497255852607

-0.405504463743171 -0.405504463743171 -0.433687043207371 -0.433687043207371

-0.07004876294422 -0.07004876294422 1.65040768571628 1.65040768571628

0.815398339875846 0.815398339875846 1.17449209706528 1.17449209706528

-0.848239940387304 -0.848239940387304 1.6354017790674 1.6354017790674

0.851760059612697 0.851760059612697 0.214498975448382 0.214498975448382 0.650407685716283 0.650407685716283

-1.1123312301194 -1.1123312301194 -0.366420800255729 -0.366420800255729 0.156311237196853 0.156311237196853

1.54585650813213 1.54585650813213 -0.140513809583606 -0.140513809583606 0.859486190416394 0.859486190416394

-0.651867903075797 -0.651867903075797 0.908125218541099 0.908125218541099

1.32222510625208 1.32222510625208 -0.464145211463651 -0.464145211463651

1.1363077980053 1.1363077980053 0.735854788536349 0.735854788536349

-0.353690482398924 -0.353690482398924 1.3354017790674 1.3354017790674

0.582218227868975 0.582218227868975 -0.045964351595226 -0.045964351595226 -0.110055641327326 -0.110055641327326 -0.725960912403672 -0.725960912403672

-0.07004876294422 -0.07004876294422 0.250407685716283 0.250407685716283 0.953582638935823 0.953582638935823

-0.676422519851506 -0.676422519851506 0.782218227868976 0.782218227868976

-0.425507902934721 -0.425507902934721 1.36585994732368 1.36585994732368

SUMMARY OUTPUT

Regression Statistics Multiple R 0.693817834786 This is the absolutue value of the correlation R Square 0.481383187867 <----------- 0.481383 "=regreession SS/total SS" Adjusted R Square 0.479642862994 Will only be observed for multiple regressions Standard Error 1.396188905273 Observations 300

ANOVA df SS MS F Significance F

Regression 1 539.198849156 539.1988 276.6054 2.15684168E-44 Residual 298 580.904350844 1.949343 Total 299 1120.1032

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 2.428449686 0.30287371917 8.018027 2.469E-14 1.832407379703 3.024492

Miles β1 0.068662036022 0.00412844384 16.63146 2.157E-44 0.060537438097 0.076787

Equation RESIDUAL OUTPUT Y_hat = 24428

Observation Predicted Time Residuals 1 9.294653288168 0.00534671183 2 5.861551487084 -1.06155148708 3 9.294653288168 -0.39465328817 4 9.294653288168 -2.79465328817 5 5.861551487084 -1.66155148708 6 7.921412567735 -1.72141256773 7 7.578102387626 -0.17810238763 8 6.891482027409 -0.89148202741 9 8.608032927952 -1.00803292795

10 8.608032927952 -2.50803292795 11 5.861551487084 1.13844851292 12 5.518241306976 1.48175869302 13 8.264722747843 1.33527725216 14 6.891482027409 -0.39148202741 15 5.174931126867 2.02506887313 16 5.861551487084 0.13844851292 17 7.578102387626 2.32189761237 18 7.578102387626 1.02189761237 19 6.891482027409 -1.99148202741 20 8.608032927952 -1.10803292795 21 8.95134310806 -1.75134310806 22 8.95134310806 0.94865689194 23 5.861551487084 -0.26155148708 24 7.921412567735 -0.42141256773

Intercept β0

25 8.608032927952 -0.80803292795 26 7.921412567735 -0.72141256773 27 7.578102387626 -0.57810238763 28 8.95134310806 -0.25134310806 29 8.608032927952 -2.20803292795 30 9.294653288168 0.60534671183 31 6.548171847301 -2.4481718473 32 8.608032927952 0.69196707205 33 7.234792207518 1.86520779248 34 9.294653288168 -0.39465328817 35 5.174931126867 0.22506887313 36 7.921412567735 -2.02141256773 37 8.608032927952 0.19196707205 38 7.921412567735 0.47858743227 39 8.95134310806 0.44865689194 40 7.578102387626 1.22189761237 41 5.174931126867 -0.17493112687 42 5.518241306976 0.98175869302 43 7.578102387626 1.12189761237 44 8.95134310806 -0.55134310806 45 6.204861667193 0.89513833281 46 7.578102387626 -1.47810238763 47 6.204861667193 -1.00486166719 48 9.294653288168 0.70534671183 49 5.861551487084 -0.76155148708 50 5.174931126867 -1.57493112687 51 8.608032927952 -0.20803292795 52 7.921412567735 -1.52141256773 53 7.921412567735 -1.22141256773 54 8.608032927952 -0.10803292795 55 6.548171847301 -0.6481718473 56 5.174931126867 -2.37493112687 57 7.234792207518 0.66520779248 58 8.95134310806 -0.05134310806 59 5.174931126867 0.82506887313 60 5.518241306976 -2.41824130698 61 5.518241306976 0.78175869302 62 6.891482027409 0.60851797259 63 8.264722747843 -1.06472274784 64 8.264722747843 -0.26472274784 65 7.578102387626 -0.77810238763 66 5.518241306976 -0.41824130698 67 5.174931126867 -1.97493112687 68 8.608032927952 -2.70803292795 69 9.294653288168 -1.49465328817 70 7.578102387626 -1.77810238763 71 5.518241306976 -1.71824130698 72 8.264722747843 -1.46472274784

73 6.548171847301 -0.8481718473 74 7.234792207518 -1.73479220752 75 8.264722747843 0.93527725216 76 7.234792207518 1.76520779248 77 8.264722747843 1.03527725216 78 8.264722747843 0.53527725216 79 5.174931126867 1.92506887313 80 8.95134310806 1.84865689194 81 5.518241306976 1.38175869302 82 8.264722747843 1.13527725216 83 5.518241306976 -1.91824130698 84 8.95134310806 -1.35134310806 85 6.891482027409 1.60851797259 86 8.264722747843 -1.16472274784 87 5.174931126867 1.92506887313 88 6.204861667193 -0.20486166719 89 5.518241306976 -0.21824130698 90 6.891482027409 -0.59148202741 91 8.264722747843 1.93527725216 92 7.578102387626 0.02189761237 93 5.174931126867 0.82506887313 94 8.264722747843 0.63527725216 95 8.264722747843 -0.66472274784 96 5.174931126867 1.42506887313 97 6.204861667193 1.79513833281 98 8.608032927952 1.09196707205 99 8.264722747843 -2.06472274784

100 5.518241306976 -1.21824130698 101 5.861551487084 -1.66155148708 102 6.548171847301 1.4518281527 103 5.518241306976 -0.01824130698 104 8.264722747843 0.63527725216 105 8.608032927952 -1.50803292795 106 5.174931126867 0.32506887313 107 7.921412567735 1.37858743227 108 7.234792207518 1.96520779248 109 7.234792207518 -0.93479220752 110 7.921412567735 0.67858743227 111 9.294653288168 1.70534671183 112 7.578102387626 -0.87810238763 113 5.861551487084 -0.36155148708 114 5.518241306976 2.58175869302 115 9.294653288168 0.90534671183 116 9.294653288168 -1.59465328817 117 7.921412567735 -0.72141256773 118 9.294653288168 -0.29465328817 119 9.294653288168 1.10534671183 120 5.518241306976 -0.41824130698

121 5.861551487084 0.53844851292 122 5.174931126867 -1.07493112687 123 9.294653288168 -1.29465328817 124 8.95134310806 -0.45134310806 125 5.861551487084 -2.26155148708 126 6.891482027409 0.40851797259 127 5.861551487084 1.03844851292 128 8.264722747843 0.43527725216 129 8.608032927952 0.19196707205 130 5.518241306976 2.78175869302 131 5.861551487084 3.43844851292 132 6.204861667193 1.29513833281 133 5.518241306976 0.18175869302 134 8.95134310806 -0.45134310806 135 6.548171847301 0.8518281527 136 6.204861667193 -0.30486166719 137 8.264722747843 -0.26472274784 138 8.95134310806 -0.25134310806 139 6.204861667193 -0.10486166719 140 5.861551487084 1.23844851292 141 5.518241306976 0.78175869302 142 5.861551487084 -0.66155148708 143 5.861551487084 0.13844851292 144 8.608032927952 -0.20803292795 145 6.891482027409 0.30851797259 146 6.548171847301 1.3518281527 147 5.174931126867 0.02506887313 148 7.921412567735 -0.92141256773 149 9.294653288168 -2.39465328817 150 7.234792207518 3.36520779248 151 8.608032927952 0.39196707205 152 7.234792207518 -1.63479220752 153 9.294653288168 -0.49465328817 154 8.264722747843 0.83527725216 155 8.608032927952 2.59196707205 156 5.174931126867 -0.97493112687 157 8.264722747843 -1.96472274784 158 5.861551487084 -2.36155148708 159 5.174931126867 2.02506887313 160 6.548171847301 -1.7481718473 161 8.264722747843 -0.36472274784 162 7.921412567735 -2.22141256773 163 5.518241306976 0.68175869302 164 9.294653288168 -2.29465328817 165 9.294653288168 2.90534671183 166 6.204861667193 -2.70486166719 167 7.234792207518 -1.53479220752 168 9.294653288168 0.70534671183

169 7.578102387626 -1.27810238763 170 5.174931126867 1.32506887313 171 7.921412567735 -0.52141256773 172 8.608032927952 -1.80803292795 173 7.578102387626 -2.17810238763 174 5.174931126867 -1.67493112687 175 5.861551487084 0.63844851292 176 8.264722747843 1.13527725216 177 5.518241306976 -0.91824130698 178 6.548171847301 1.7518281527 179 7.921412567735 0.57858743227 180 6.204861667193 -0.40486166719 181 6.204861667193 0.49513833281 182 8.608032927952 0.29196707205 183 5.174931126867 -0.17493112687 184 7.921412567735 -0.62141256773 185 5.174931126867 0.72506887313 186 6.548171847301 -0.5481718473 187 8.608032927952 1.29196707205 188 6.204861667193 -0.50486166719 189 7.578102387626 -1.87810238763 190 6.204861667193 0.59513833281 191 6.891482027409 0.70851797259 192 5.518241306976 -0.51824130698 193 8.264722747843 2.83527725216 194 8.264722747843 -0.56472274784 195 6.891482027409 1.60851797259 196 9.294653288168 0.70534671183 197 5.174931126867 0.92506887313 198 6.204861667193 0.79513833281 199 8.608032927952 1.49196707205 200 5.861551487084 -1.26155148708 201 6.891482027409 -1.39148202741 202 7.921412567735 -1.62141256773 203 7.234792207518 -1.03479220752 204 7.234792207518 1.26520779248 205 8.95134310806 2.54865689194 206 5.861551487084 3.53844851292 207 8.608032927952 -0.10803292795 208 6.548171847301 -0.4481718473 209 7.921412567735 -2.62141256773 210 8.95134310806 2.04865689194 211 8.264722747843 0.13527725216 212 6.548171847301 -0.3481718473 213 5.518241306976 -0.51824130698 214 8.264722747843 -2.56472274784 215 8.264722747843 -1.46472274784 216 5.861551487084 -1.36155148708

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