All information is provided below. Entire question and f and t distribution tables.
Exercise 15.19 Algo (Testing for Significance) The following estimated regression equation is based on 10 observations was presented. 1 = 29.1270 + 0.590601 + 0.49802 Here SST = 6,686.125, 88R = 6,076.750, #b, = 0.0876, and #6, = 0.0626- a. Compute MBR and MSE (to 3 decimals). MSR = MSE = b. Compute F and perform the appropriate F test (to 2 decimals). Use a = 0.06. Use the F table. F= The p-value is less than 0.01 At a = 0.05, the overall model is significant C. Perform a t test for the significance of 81 (to 2 decimals). Use a = 0.06. Use the t table. to = The p-value is less than 0.01 At a = 0.05, there is a significant relationship between y and $1. d. Perform a t test for the significance of 8, (to 2 decimals). Use a = 0.06. Use the t table. The p-value is less than 0.01 At o = 0.05, there is a significant relationship between y and y.TABLE 4 F DISTRIBUTION Area or probability Fa Entries in the table give F. values, where a is the area or probability in the upper tail of the F distribution. For example, with 4 numerator degrees of freedom. 8 denominator degrees of freedom, and a .05 area in the upper tail, F = 3.84. Demminator Are in Numeroior Degrees of Freedom Degrees Upper of Freedom Tail 1 3 5 6 7 9 10 15 20 25 100 40 50 53.59 57.24 58.20 58.91 50 44 60.19 61.21 61.74 62.05 62 26 62 53 62.79 63.01 DE 19 161.45 199.50 215.71 230.16 233.99 236.77 240.54 245.95 248 02 249.16 250.10 251.14 252 20 253.04 254.19 025 647.79 70.48 864.15 048.20 956.64 984.87 1001.40 1015.40 1009.79 1013.16 1017.76 4052.18 4919.34 5403.53 5624.26 5763.96 5858.95 5928 33 5960.95 6022.10 6055.93 6156.97 6208.66 6239.56 6260 35 6256.43 6312 97 6333.92 6362.80 9.24 0:20 0.42 10.40 05 18.51 19.16 19.25 19.30 19 3 19.35 19 37 19.39 19:40 19/43 19.45 19.46 194 19.47 1948 19/49 30 40 30 50 LO DE 39,17 30.25 DE DE LE DE 30 16 LE GE DE DE 30 40 39.45 30 46 39 46 10 47 90.47 04 50 01 98.50 90.25 90.40 90.43 09.45 90.46 5.54 5.46 5.31 5.27 5.20 5.17 5.17 $.16 5.15 5.13 05 0.12 901 8.40 8.85 8.70 H.70 8 55 853 10.13 055 0.28 8 62 025 17.44 16.04 15.44 15.10 14.73 14.62 1454 14.47 14.42 14.25 14.17 14.12 14 06 14.04 13.04 13.91 34.12 30.82 2946 28.71 28.24 17.91 27.67 27.49 27.34 27.23 26.87 26.169 26 58 26.50 26.41 26.32 26.24 26.14 4.54 4.32 4.19 4.1I 405 3.95 3.92 3.87 3.84 3.83 3.82 3.80 3.79 3.78 3.76 5.63 05 7.71 6.94 6.59 6.39 6.26 6.16 609 6.04 6.00 5.96 5.86 5.80 5.77 5.75 5.72 5.69 5.66 12 72 9 36 0 20 8 46 841 8.36 .DI 21.20 18.00 16.60 15.96 15.52 15.21 148 14.80 14.66 4.55 14.20 14.02 13.91 1384 13.75 3.65 1358 13.47 4.06 3.52 345 3.40 3 37 3 34 3 30 3 374 3.21 3,19 3. 16 3,13 3.11 10 3.78 3,67 1.14 6.61. 5.79 5.41 5.19 505 4.82 4.37 4.74 462 456 452 4.50 4.46 4.43 4.41 4.37 025 10.01 8.43 7.76 7.30 7.15 6.98 6.76 6.68 6.62 6.43 6.33 6.27 6.23 6.18 6.12 6.02 16.26 13.27 1206 11.39 10.97 10 67 10:46 10 29 10.16 10.05 9 72 455 9 45 9 38 9 70 0. 13 903TABLE 4 F DISTRIBUTION (Continued) Denominator Area in Numerator Degrees of Freedom Degrees Upper ICH In 15 M of Freedom Tal I 2 3 4 7 2.76 275 2.72 3.70 3.46 3.29 3.18 3.11 3.05 3.01 2:95 296 294 2.81 2.80 3.77 1.74 3.71 3.67 5.99 5.14 4.76 4.53 4.30 4.26 4.21 4.10 4.06 3.94 3.47 3.83 3.81 4.82 5.46 5.27 5.17 5.11 501 402 7.26 6.60 5.23 7.73 7.14 13.75 10192 9.78 9.15 8.75 B.47 8.26 7.56 2.50 254 250 247 2 70 263 251 275 251 2.56 T .10 3.39 3.IT 206 2. HH 3.23 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.51 3.44 3.40 3.38 3.34 3.30 3.27 4.25 4.21 4.15 025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4:90 4.82 4.76 4.57 4.47 4.40 436 4.31 571 6.31 6.16 5.00 3.75 12.1 3.45 T.HS 7.46 7.19 2.54 2.46 2.42 2.34 2.32 230 .10 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 3.11 3.0 304 2.07 2.01 5.32 4.46 4.m 1.44 3.22 1.15 4.10 400 3.94 3.84 3.78 3.74 3.68 025 757 6006 5.42 5.05 4.81 4.45 4.53 4.43 4.36 4.30 5.12 5.03 1.96 1.87 .DI 11.26 8.65 7.59 7.01 6.63 637 5.18 5.91 5.81 5.57 5.36 5.20 2.61 2.55 2.51 2.47 2.44 241 2.34 230 2.21 2.25 2.23 221 2.19 2.10 .10 3.36 3.01 2.81 2.69 3.14 3.01 2.94 2.80 2.86 2.83 2.79 2.76 2.71 105 5.12 4.26 3.86 3.63 3.48 3.37 3.21 3.18 3.77 3,60 1 56 3.51 1.40 3.14 3.96 035 7.21 5.71 4.77 4.37 4.20 4.10 4,03 5.61 4.81 4.71 145 457 4.41 142 10.56 8.02 5.06 5.80 2.16 2.13 211 2.09 206 10 .10 3.29 2.92 1.73 2.61 2.51 2.46 2.41 2.32 2.35 2.32 2.24 230 2.17 2.85 277 2.73 2.70 2.46 262 254 4.96 4.10 3.71 3.48 3.31 3.22 3.14 2.98 3.15 309 015 6.94 5.46 4.83 4.47 4.07 3.95 3.85 3.78 3.72 3.52 3.42 3.35 3.31 3.16 3.20 5.30 5,06 456 4 41 4.31 4.17 401 10.04 756 5.90 3.64 5,39 2.05 2103 2.01 198 .10 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 2.17 2.12 2.10 208 241 4.84 3.50 3.16 3.20 3.04 3.01 295 2.90 2.85 2.72 265 257 2 40 246 3.50 3.53 3.33 3.23 3.16 3.17 035 6.72 3.26 4.63 4 78 4,04 3.#8 3,TE 3.66 3.71 9.65 7.21 5.47 510 5.07 4.30 1.74 4.54 4.25 401 191 3.18 281 2.61 148 2.30 2.39 2.18 2.14 2.21 2.19 2.10 206 201 1.94 1.46 1.94 12 -10 2.30 4.75 3.89 3.40 3.11 3.00 2.01 2.85 2.30 2.75 2.62 2.54 2.50 2AT 2.43 2 30 2.35 3.37 3.18 3.07 3.01 2.96 2.91 2.60 2.73 025 655 5.10 4.47 4.12 3.69 3.73 3.61 351 3.44 354 3.47 3 37 EL G 4.87 4.FA 4.30 4.30 401 170 3.67 2.20 2.16 2.14 205 2.01 1.98 1.96 1.93 1.90 1.85 13 .10 3.14 2.76 2.56 2.43 2.35 2.18 2.13 3,18 3.03 2.92 2.83 2.77 2.71 2.67 7.53 2 46 241 2.36 234 2 26 4 67 3.81 3.41 2.88 2.78 271 267 2.60 1025 641 4.97 4.35 400 3.77 3.60 3.48 3.39 3.31 3.25 306 295 9.07 6.70 5.74 5.21 4.44 4.30 4.19 3.82 3.66 3.57 3.51 3.43 3.77 2.15 212 2.10 201 1.96 1.93 1.90 1.89 1.86 14 .10 3.10 273 2.52 2.34 231 2.24 2.19 265 2.60 2.46 2.39 2.34 2.31 2.27 2.21 2.19 214 05 4.60 334 2.96 2.85 2.76 2.70 3.38 3.29 3.21 3.15 2.95 2.84 2.76 2.73 2.67 2.61 256 750 025 6.30 4.86 4.24 3.89 3.66 3.50 3.04 351 341 3.35 3.17 3.18 3.11 8.86 651 3.56 4 ED 4.46 4 28 4.14 403 3.56 I.KT 1.85 1.61 179 1.76 13 3.07 2.70 249 217 211 2.16 2.12 2.09 1.92 1.39 454 3.70 3.06 2 90 2 70 271 264 240 24 2 40 2.33 278 2.25 2.20 2.16 2.12 207 158 3.41 3.29 3.20 3.12 2.86 2.76 2 69 2.64 250 2.57 2.47 2.40 025 6.20 4.77 4.15 4.00 3.89 3.80 3.37 3.28 3.21 3.13 298 6.36 $ 42 1 20 4 56 4 32 4.14Denominaior Area in Numerator Degrees of Freedom Degrees Upper Tail fi 25 LE of Freedom 4 7 3.05 2.67 2.46 2.33 1.M4 2.18 2.13 2.09 2.06 2.03 1.94 1.89 1.86 1.78 1.76 1.72 4.19 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.35 2.28 2.21 2.19 2.15 2.11 2.07 202 6.12 4.60 3.71 3.14 3.27 3,12 3.05 209 2.79 2.61 247 245 2.40 5.29 1.77 4.14 3.50 3.TH 3.41 3.26 3.16 203 176 17 1.03 2.64 244 231 2.15 2.10 2.06 2.03 2.0 1.91 1.86 1,75 1.73 105 4.45 3.59 3.20 2.96 2.81 2.70 1.61 2.55 2.49 2.45 2.31 121 2.18 215 2.10 206 2.02 025 5.04 4.62 4.01 3.66 3.44 3.28 3.16 3/06 2.96 2.92 2.12 2.61 2.55 2 50 2.44 238 2.33 2.26 6.II 5.19 4.67 4.10 3.70 3.68 3.50 3.31 3,16 3.07 .00 102 2.76 2 65 3.01 2.62 2.42 2.29 2.20 2.13 208 2.00 1.98 189 1.84 1.80 I.78 1.75 1.72 1.70 1.65 4.41 345 3,16 2.07 3.77 2.F6 241 246 2.41 217 2.19 2.14 2.11 206 202 I ON 1.92 456 3.05 3.61 3.10 3.01 2.93 2.87 2.67 2.40 244 232 2 20 025 8 29 6.01 5.00 4.58 4.25 3.84 3.71 3.60 351 3.23 298 2101 2.75 2.68 -10 2.90 2.81 2.40 2.27 2.18 2.11 1 98 1.06 1.86 1.81 1.78 1.76 1.73 1.70 167 1.64 05 4 38 3.52 1.13 2.90 2.74 2.54 2.48 242 2.38 2.23 2.16 211 2.07 2.00 1.94 1.88 025 5.92 4.51 3.90 3.56 3.33 3.17 305 2.96 2.88 2.82 2.62 2.51 244 2.39 2.33 2.27 2.27 2.14 4.17 3.04 3.77 142 143 201 2 84 276 2.67 20 297 259 2.38 2.25 2.16 2109 2.00 196 1.94 184 1.79 1.76 1.74 1.71 1.61 340 3.10 2 87 271 251 245 235 2.20 2.12 2 07 2/04 1.95 1.91 025 4.46 351 3.20 3.13 301 291 284 217 2.57 2.46 2.40 2.35 2 20 2.12 217 5.85 4.43 3.47 3.70 3.56 3.46 3.37 3.09 294 284 2.78 2.61 2.54 2.43 1.G6 1.63 1.50 21 -10 2.96 257 2.23 2.14 208 202 1.98 195 1.92 1.83 1.78 1.74 1.12 1.32 347 307 2.84 2 68 257 2.40 2.42 2.37 232 2.10 205 2.01 146 1.92 1.82 4.42 1.82 348 3.25 2 87 2.80 273 253 2.42 2.36 2.31 2.25 2.18 2.13 2.05 ANT 404 3.81 351 340 321 3.03 270 2.12 264 245 256 235 2 27 213 201 1.47 1.03 1 90 I.HI 1,76 1.73 1,TO L 67 1.64 1.61 1.57 4.30 3.44 305 282 2 66 246 234 2.30 215 2.07 202 1.98 1.04 1.80 1.70 025 5.79 1.38 3.78 3.41 3.22 3.05 293 276 2.70 2.50 2.39 2.32 2.17 2.21 2.14 209 2.01 7.Os 5.72 4.82 4.31 3 76 345 1.35 2.83 273 2.67 242 10 294 2.55 234 221 211 205 1.94 1.95 1.92 1.89 1.80 1.74 1.71 1.66 1.62 1.59 135 4.28 3.47 3.03 2.80 2.64 253 2.44 2.37 232 2.27 2.13 2.06 2.00 1.96 1.91 1.82 1.76 025 5.75 4.35 3.75 3.18 3.01 290 2.81 273 267 2.36 2.29 2.14 218 2.11 206 5.66 1.76 4.26 3104 3.41 3.30 201 2.78 2.62 254 245 2.37 1.17 24 10 201 254 231 210 2.10 204 1.04 1.91 1.78 1.73 1.70 1.67 161 154 05 4.26 3.40 3.01 2.78 2.62 2.51 2.41 2.30 2.25 2.11 2.00 1.97 1.94 1.89 1.80 1.74 025 5.72 4.31 3.71 3.38 3.15 2.90 2.87 2.78 2.70 264 2.41 2.33 2.26 2.21 2.15 2.02 1.94 5.6 4.71 4.22 3,67 1.50 1.36 3.26 3.17 2.74 2 64 258 .40 2 40 7.33 2 72TABLE 4 F DISTRIBUTION (Continued) Denominator Area in Numerator Degrees of Freedom Upper of Freedom Tail 3 4 5 7 10 15 40 .10 2.92 253 218 201 1.01 1.89 1.77 1.12 1.63 1.50 1.56 152 05 4.24 3.39 209 276 249 240 234 2.28 2.M 209 2.01 1.96 1.92 I.ST 1.82 1.78 1.72 420 3.35 3.13 207 2 85 275 261 241 2.18 212 205 1.91 7.71 5.57 4.18 3.85 3.21 3.13 2.85 2.70 254 245 2.18 ,10 2.31 217 201 1.96 1.91 1.86 1,76 1.65 1.61 1.45 151 105 3.37 274 247 232 2.27 2.22 1.90 1.04 1.90 1.85 1.80 1.76 1.70 025 5.66 4.27 3.67 3.10 2.04 2.81 273 2.65 2.50 2.39 2.28 2.21 2.16 2.09 1.97 7.72 5.53 4.14 3.82 3.42 3.20 3.13 3.0P 2.81 2.65 257 2.50 242 2.33 2.25 2.14 27 .10 2.90 2.51 2.30 2.17 2.07 20 1.95 1.91 1.67 1.85 1.75 1.70 1.66 1.64 1.57 154 1.50 05 4.21 3.35 2.71 2.46 237 2.31 2.25 2.20 206 197 1.74 4.34 3.31 2.91 2. 80 2.71 257 2.36 2.25 218 213 207 200 1.94 1 36 5.14 4.11 3.56 3.39 3.26 3.15 3.06 2.78 2.54 247 2.20 2.12 2.16 20 1.94 1.57 1,74 1.65 1.63 1.56 105 4.20 3.34 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.04 1.96 191 187 1.81 1.77 1.73 1 66 025 5.61 4.21 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 234 2.23 2.16 2II 2.05 1.98 1.92 7.44 4.45 3.36 3:21 3.12 3.08 2.75 2.60 241 244 2 26 2.19 208 10 2.50 2.20 2.15 2.0 1.99 1.93 1.73 1.6 1.62 158 1.53 1.52 4.18 2.01 2.70 255 ETZ 2.35 2.28 2.27 2.18 203 1.04 1.75 1.TI 1.65 025 4:20 3.61 3.17 3.04 2.T6 2.67 2 50 2.32 2.21 2.14 209 FONZ 1.06 1.90 1.82 7.40 5.42 3.73 3.50 3.33 3.20 3.09 3.00 2.73 2.57 248 241 2.33 123 2.16 205 .10 2.49 2.14 2105 1.50 1.90 1.28 1.85 1.82 1.72 1.67 1.63 157 1.54 151 1.46 105 4.17 2.92 2.49 2.53 2.42 2.33 2.17 2.21 2.16 2.01 1.93 1.84 1.79 1.74 1.70 1.63 035 3.50 3.75 3.03 287 2.75 2.65 2.57 251 231 2.20 2.12 201 1.04 756 402 3.70 3.47 3.30 3.17 2.70 2.45 2.30 2.21 2.13 -10 2.34 2.44 2.23 2.00 1.93 187 1.79 1.76 1.66 1.61 1.57 1.54 131 L.AT 1.43 138 408 3.23 2.84 161 2.45 2.34 2.25 2.18 2.12 2.08 1.92 1.84 1.78 1.74 1.64 1.50 1.51 025 5.42 1.05 3.46 3.13 2.90 2.74 262 2.53 2.45 2.39 2.18 2.07 1.99 1.94 18B 1.80 1.74 1.65 731 5.18 151 3.29 3.12 2.90 2.80 2.80 2.52 2.37 2.27 2.20 2.11 2.01 1.94 1.81 -10 2.79 139 2.18 195 1.87 1.82 1.77 1.74 1.71 1.60 1.54 1.50 1.48 1.44 1.36 1.30 05 4,00 3.15 2.76 253 2 37 2.25 2.17 2.10 2.04 1 99 1.75 1.60 1.65 1.59 1.53 1/40 025 3.01 2.79 2.63 251 241 2.33 2.27 206 1.94 1.27 1.74 1.60 1.49 314 3.12 2.05 282 2.72 235 2.20 2.10 1.94 1.84 1.75 1.62 2.76 2 16 214 191 1.83 1.78 1.73 1.69 166 1.56 1.49 145 1.42 1.38 1.34 1.20 1.12 304 2.70 246 231 2.19 2.10 203 1.97 103 1.77 1.68 1.62 1.57 1.52 1.45 1.39 1.30 025 5.18 3.83 1.25 292 2.70 254 242 2.32 224 2.18 1.97 1.77 1.71 1.56 1.36 351 3.71 282 2 50 2.07 1 97 1.60 1.45 1040 2.71 231 209 1.95 1.85 1.78 1.72 1.61 1.49 143 1.38 1.35 1.30 1.25 1.20 1.08 3 85 3.00 2 61 238 2 22 211 202 1.95 1.58 1.52 1.47 1.41 1.33 1.26 025 504 370 313 2.80 258 242 230 2.20 213 206 1.85 1.72 1.64 1.58 1.50 141 1.32 1.13 .01 6.66 463 3.80 1.04 182 2.66 2.53 2.43 234 206 1.90 1.79 1.72 1.61 150 1.38 1.16TABLE 2 DISTRIBUTION Area or probability Entries in the table give values for an area or probability in the upper tail of the distribution. For example, with 10 degrees of freedom and a .05 area in the upper tail, Area in Upper Tail of Freedom 20 A0 05 025 A1 D05 I 1.376 3.078 6.314 12.706 31.821 63.656 2 1.061 1.886 2.920 4.303 6.965 9.925 3 978 1.638 2.353 3.182 4.541 5.841 4 941 1.533 2,132 2.776 3.747 4.604 5 920 1.476 2.015 2.571 3.365 4.032 6 906 1.440 1.943 2447 3.143 3.707 7 896 1.415 1.895 2.365 2.998 3499 8 889 1.397 1.860 2.306 2.896 3.355 9 883 1.383 1.833 2.262 2821 3.250 10 879 1.372 1.812 2228 2.764 3.169 11 876 1.363 1.796 2201 2718 3.106 12 873 1.356 1.782 2.179 2.681 3.055 13 .870 1.350 1.771 2.160 2.650 3.012 14 .B68 1.345 1.761 2.145 2.624 29717 15 866 1.341 1.753 2.131 2.602 2.947 16 865 1.337 1.746 2.120 2.583 2.921 17 863 1.333 1.740 2.110 2.567 2.898 18 862 1.330 1.734 2.101 2552 2878 19 861 1.328 1.729 2093 2539 2.861 \f\f
