Hypothesis Test linear regression: To determine the validity and reliability of the best-fit line, a hypothesis test
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Hypothesis Test linear regression: To determine the validity and reliability of the best-fit line, a hypothesis test can be conducted. The type of test and the level of significance must be specified. The necessary computations include obtaining the critical value and the test statistic, which is used to determine the t value.
hypothesis
type of test/level of significance, decision rule, test statistics, results and conclusion
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FIGURE 1.1 X 7.6 Y - - Data for pH (X) and bicarbonate concentration (Y) wells in NorthWest Texas xi-xbar yi-ybar (xi-xb)(yi-(xi-xbar) (yi-ybar] y hat | yh yb: (yh yb]^{ yi-y hal (yi yh]^2 157 -0.062 14.206 -0.877422 0.00381 201.807 145.13 2.3326 5.441006 11.873 140.9749 174 -0.562 31.206 -17.53036 0.31558 973.807 164.01 21.216 450.0983 9.9904 99.80733 175 0.5382 32.206 17.33434 0.2897 1037.22 122.47 -20.33 413.1834 52.533 2759.695 188 -0.162 45.206 -7.312716 0.02617 2043.57 148.9 6.1092 37.3221 39.097 1528.552 171 -0.262 28.206 -7.383304 0.06852 795.572 152.68 9.8858 97.72837 18.32 335.6267 143 0.1382 0.2059 0.02846 0.01911 0.04239 137.57 -5.221 27.25438 5.4265 29.44642 217 -0.362 74.206 -26.84507 0.13087 5506.51 156.46 13.662 186.6598 60.544 3665.519 190 0.3382 47.206 15.9667 0.1144 2228.4 130.02 -12.77 163.1685 59.98 3597.555 142 -0.562 -0.794 0.446107 0.31558 0.63062 164.01 21.216 450.0983 -22.01 484.4242 190 -0.162 47.206 -7.636246 0.02617 2228.4 148.9 6.1092 37.3221 41.097 1688.939 215 0.4382 72.206 31.64317 0.19205 5213.69 126.24 -16.55 273.9133 88.756 7877.665 199 -0.662 56.206 -37.19507 0.43793 3159.1 167.79 24.992 624.6053 31.214 974.2999 262 -0.362 119.21 -43.12448 0.13087 14210 156.46 13.662 186.6598 105.54 11139.44 105 0.1382 -37.79 -5.224481 0.01911 1428.4 137.57 -5.221 27.25438 -32.57 1061.036 121 -0.362 -21.79 7.884343 0.13087 474.984 156.46 13.662 186.6598 -35.46 1257.161 81 0.3382 -61.79 -20.90095 0.1144 3818.51 130.02 -12.77 163.1685 -49.02 2402.997 82 0.8382 -60.79 -50.95978 0.70264 3695.92 111.14 -31.66 1002.145 -29.14 848.991 210 -0.562 67.206 -37.75389 0.31558 4516.63 164.01 21.216 450.0983 45.99 2115.113 59.206 31.8667 0.2897 3505.34 122.47 -20.33 413.1834 79.533 6325.465 12.206 2.907872 0.05676 148.984 133.8 -8.997 80.94885 21.203 449.5689 0.00381 201.807 145.13 2.3326 5.441006 11.873 140.9749 147 1.1382 4.2059 4.787284 1.29558 17.6894 99.808 -42.99 1847.832 47.192 2227.114 -0.462 -9.794 4.522578 0.21323 95.9247 160.23 17.439 304.1165 -27.23 741.6392 53 0.2382 -89.79 -21.39213 0.05676 8062.98 133.8 -8.997 80.94885) -80.8 6528.149 56 0.4382 -86.79 -38.03625 0.19205 7533.22 126.24 -16.55 273.9133 -70.24 4934.19 -29.79 -1.139187 0.00146 887.689 141.35 -1.444 2.085102 -28.35 803.7298 35 0.7382 -107.8 -79.57742 0.54499 11619.6 114.91 -27.88 777.299 -79.91 6386.253 0.06852 316.631 152.68 9.8858 97.72837 -27.68 766.176 0.13087 4461.45 156.46 13.662 186.6598 -80.46 6473.243 0.70264 8985.92 111.14 -31.66 1002.145 -63.14 3986.338 0.01911 17.6894 137.57 -5.221 27.25438 9.4265 88.85806 0.92499 665.337 179.12 36.322 1319.278 -62.12 3858.395 0.31558 1537.1 164.01 21.216 450.0983 17.99 323.6531 0.13087 3112.98 156.46 13.662 186.6598 -69.46 4824.201 -313.4676 8.30029 102704 394.38 11838.37 90865.19 rsquare= 0.11527 7.1 8.2 7.5 7.4 7.8 7.3 8 7.1 7.5 8.1 7 7.3 7.8 7.3 8 8.5 7.1 8.2 202 0.5382 7.9 155 0.2382 7.6 157 -0.062 8.8 7.2 133 7.9 8.1 7.7 113 0.0382 8.4 7.4 125 7.3 8.5 76 7.8 6.7 7.1 7.3 7.6618 48 0.8382 -94.79-79.45978 147 0.1382 4.2059 0.581401 117 -0.962 -25.79 24.80787 182 -0.562 39.206-22.02448 87 -0.362-55.79 20.18434 142.79 b1= -37.77 60= 432.15 14.206-0.877422 -0.262 -17.79 4.657872 -0.362-66.79 24.16375 FIGURE 1.1 X 7.6 Y - - Data for pH (X) and bicarbonate concentration (Y) wells in NorthWest Texas xi-xbar yi-ybar (xi-xb)(yi-(xi-xbar) (yi-ybar] y hat | yh yb: (yh yb]^{ yi-y hal (yi yh]^2 157 -0.062 14.206 -0.877422 0.00381 201.807 145.13 2.3326 5.441006 11.873 140.9749 174 -0.562 31.206 -17.53036 0.31558 973.807 164.01 21.216 450.0983 9.9904 99.80733 175 0.5382 32.206 17.33434 0.2897 1037.22 122.47 -20.33 413.1834 52.533 2759.695 188 -0.162 45.206 -7.312716 0.02617 2043.57 148.9 6.1092 37.3221 39.097 1528.552 171 -0.262 28.206 -7.383304 0.06852 795.572 152.68 9.8858 97.72837 18.32 335.6267 143 0.1382 0.2059 0.02846 0.01911 0.04239 137.57 -5.221 27.25438 5.4265 29.44642 217 -0.362 74.206 -26.84507 0.13087 5506.51 156.46 13.662 186.6598 60.544 3665.519 190 0.3382 47.206 15.9667 0.1144 2228.4 130.02 -12.77 163.1685 59.98 3597.555 142 -0.562 -0.794 0.446107 0.31558 0.63062 164.01 21.216 450.0983 -22.01 484.4242 190 -0.162 47.206 -7.636246 0.02617 2228.4 148.9 6.1092 37.3221 41.097 1688.939 215 0.4382 72.206 31.64317 0.19205 5213.69 126.24 -16.55 273.9133 88.756 7877.665 199 -0.662 56.206 -37.19507 0.43793 3159.1 167.79 24.992 624.6053 31.214 974.2999 262 -0.362 119.21 -43.12448 0.13087 14210 156.46 13.662 186.6598 105.54 11139.44 105 0.1382 -37.79 -5.224481 0.01911 1428.4 137.57 -5.221 27.25438 -32.57 1061.036 121 -0.362 -21.79 7.884343 0.13087 474.984 156.46 13.662 186.6598 -35.46 1257.161 81 0.3382 -61.79 -20.90095 0.1144 3818.51 130.02 -12.77 163.1685 -49.02 2402.997 82 0.8382 -60.79 -50.95978 0.70264 3695.92 111.14 -31.66 1002.145 -29.14 848.991 210 -0.562 67.206 -37.75389 0.31558 4516.63 164.01 21.216 450.0983 45.99 2115.113 59.206 31.8667 0.2897 3505.34 122.47 -20.33 413.1834 79.533 6325.465 12.206 2.907872 0.05676 148.984 133.8 -8.997 80.94885 21.203 449.5689 0.00381 201.807 145.13 2.3326 5.441006 11.873 140.9749 147 1.1382 4.2059 4.787284 1.29558 17.6894 99.808 -42.99 1847.832 47.192 2227.114 -0.462 -9.794 4.522578 0.21323 95.9247 160.23 17.439 304.1165 -27.23 741.6392 53 0.2382 -89.79 -21.39213 0.05676 8062.98 133.8 -8.997 80.94885) -80.8 6528.149 56 0.4382 -86.79 -38.03625 0.19205 7533.22 126.24 -16.55 273.9133 -70.24 4934.19 -29.79 -1.139187 0.00146 887.689 141.35 -1.444 2.085102 -28.35 803.7298 35 0.7382 -107.8 -79.57742 0.54499 11619.6 114.91 -27.88 777.299 -79.91 6386.253 0.06852 316.631 152.68 9.8858 97.72837 -27.68 766.176 0.13087 4461.45 156.46 13.662 186.6598 -80.46 6473.243 0.70264 8985.92 111.14 -31.66 1002.145 -63.14 3986.338 0.01911 17.6894 137.57 -5.221 27.25438 9.4265 88.85806 0.92499 665.337 179.12 36.322 1319.278 -62.12 3858.395 0.31558 1537.1 164.01 21.216 450.0983 17.99 323.6531 0.13087 3112.98 156.46 13.662 186.6598 -69.46 4824.201 -313.4676 8.30029 102704 394.38 11838.37 90865.19 rsquare= 0.11527 7.1 8.2 7.5 7.4 7.8 7.3 8 7.1 7.5 8.1 7 7.3 7.8 7.3 8 8.5 7.1 8.2 202 0.5382 7.9 155 0.2382 7.6 157 -0.062 8.8 7.2 133 7.9 8.1 7.7 113 0.0382 8.4 7.4 125 7.3 8.5 76 7.8 6.7 7.1 7.3 7.6618 48 0.8382 -94.79-79.45978 147 0.1382 4.2059 0.581401 117 -0.962 -25.79 24.80787 182 -0.562 39.206-22.02448 87 -0.362-55.79 20.18434 142.79 b1= -37.77 60= 432.15 14.206-0.877422 -0.262 -17.79 4.657872 -0.362-66.79 24.16375
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