cum. prob one-tail 1.50 1.75 1.80 1.85 1.90 1.95 1.975 1.99 1.995 1.999 t.9995 0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 two-tails 1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001 df 1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.31 636.62 2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 6.965 9.925 22.327 31.599 5.841 10.215 12.924 4 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 9 89 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 4.501 5.041 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 16 56 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 0.000 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768 25 27 28 29 30 40 22222234 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 0.000 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.690 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 0.000 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.659 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460 80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639 3.195 3.416 100 0.000 0.677 0.845 1.042 1.290 1.660 1.984 2.364 2.626 3.174 3.390 1000 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581 3.098 3.300 Z 0.000 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291 0% 50% 60% 70% 80% 90% 95% 98% 99% 99.8% 99.9% Confidence Level
Table 1 - San Francisco Bread Company (30 Markets)
Demand Price Competitor Advertising Income
Market (Q) (P) Price (Px) (Ad) (I)
1 596,611 7.62 6.52 200,259 54,880
2 596,453 7.29 5.01 204,559 51,755
3 599,201 6.66 5.96 206,647 52,955
4 572,258 8.01 5.30 207,025 54,391
5 558,142 7.53 6.16 207,422 48,491
6 627,973 6.51 7.56 216,224 51,219
7 593,024 6.20 7.15 217,954 48,685
8 565,004 7.28 6.97 220,139 47,219
9 596,254 5.96 5.52 220,215 49,775
10 652,880 6.42 6.27 220,728 54,932
11 596,784 5.94 5.66 226,603 48,092
12 657,468 6.47 7.68 228,620 54,929
13 519,866 6.99 5.10 230,241 46,057
14 612,941 7.72 5.38 232,777 55,239
15 621,707 6.46 6.20 237,300 53,976
16 597,215 7.31 7.43 238,765 49,576
17 617,427 7.36 5.28 241,957 55,454
18 572,320 6.19 6.12 251,317 48,480
19 602,400 7.95 6.38 254,393 53,249
20 575,004 6.34 5.67 255,699 49,696
21 667,581 5.54 7.08 262,270 52,600
22 569,880 7.89 5.10 275,588 50,472
23 644,684 6.76 7.22 277,667 53,409
24 605,468 6.39 5.21 277,816 52,660
25 599,213 6.42 6.00 279,031 50,464
26 610,735 6.82 6.97 279,934 49,525
27 603,830 7.10 5.30 287,921 49,489
28 617,803 7.77 6.96 289,358 49,375
29 529,009 8.07 5.76 294,787 48,254
30 573,211 6.91 5.96 296,246 46,017
Mean 598,412 6.93 6.16 244,649 51,044
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.91280128
R Square 0.83320617
Adjusted R Square 0.80651916
Standard Error 14865.8981
Observations 30
ANOVA
df SS MS F Significance F
Regression 4 27599092617.3 6.9E+09 31.22141 2.1613677E-09
Residual 25 5524873170.172 2.21E+08
Total 29 33123965787.47
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 128740.913 69966.78193792 1.840029 0.077667 -15358.270428 272840.097 -15358.27043 272840.09727
X Variable 1 -19864.901 4102.111195403 -4.842604 5.6E-05 -28313.351546 -11416.451 -28313.35155 -11416.45108
X Variable 2 15484.5544 3459.19312176 4.476349 0.000145 8360.2178349 22608.891 8360.2178349 22608.891043
X Variable 3 0.26006502 0.093982856319 2.767154 0.010486 0.0665038381 0.4536262 0.0665038381 0.4536261986
X Variable 4 8.78206805 1.016513087275 8.639405 5.62E-09 6.6885216251 10.8756145 6.6885216251 10.875614477
Table 2 - Estimated Demand Function for the
San Francisco Bread Company
Estimated Standard Error
Variable Coefficient of Coefficient t-statistic
(1) (2) (3) (4) = (2) / (3)
Intercept 128,740.913 69,966.782 1.840
Price (P) -19,864.901 4,102.111 -4.843
Competitor P 15,484.554 3,459.193 4.476
Advertising ( 0.260 0.094 2.767
Income (I) 8.782 1.017 8.639
F Statistic = 31.221
Standard Error of the Estimate = SSE = 14,865.898
Coefficient of Determination: R2 = 83.3%
Question: solve the below using the T-statistics
Describe the level statistical significance for each individual independent variable
included in the San Francisco demand equation. Develop the null and alternative
hypothesis for each variable.
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