ECO220Y5 Chapter Notes - Chapter 14: Central Limit Theorem, Null Hypothesis, Standard Deviation
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1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.
Quarter Seasonal Index Seasonally Adjusted Data
Q1 .80 295
Q2 .85 299
Q3 1.15 270
Q4 --- 271
2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?
A. Alpha and Delta
B. Delta and Gamma
C. Alpha and Gamma
D. Standard Deviation and Mean
3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.
A. Ho: r = .05 p < .5
B. Ho: r = 0 p >.05
C. Ho: r ? 0 p?.05
D. Ho: r = 0 p?.05
In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable? |
A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.
5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied? |
A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right
A. The rejection region and the t-table value generally gets smaller for sample size below 31. |
A. Yes. The data are significantly correlated through the 12th lag. C. No. Only the 12 lag period is not correlated. D. You cannot tell since the number of sample observations is not provided. E. The p-value is above .05 so the data is correlated. |
A. Type 2 error |
A. Yes. They move in the same direction as statistical significance. |
A. The weight cannot be calculated since the data observation is not given. |
A. Yes. The correlation coefficient is .873 that is greater than .05. |
A. Yes, since the residuals randomly vary in magnitude. |
A. -101.0 |
|
The data for this assignment comes from household surveys carried out on a small island in Eastern Indonisa. The island, Selayar Island, is located in South Sulawesi, has two main industries: fishing and agriculture. We will be focusing of fishing activities occurring nearshore. Nearshore fishing takes place over coral reef, seagrass, and mangrove habitat. The most common fishing gear include spear guns, pole and lines, and nets. The boats used for fishing range from small canoes to small boats. The data was collected using a randomn sampling technique, and includes 152 fishing households.
Each fishing household was allowed to describe up to 6 different types of fishing trips. Researchers collected information on the âaverge tripâ. A subset of the data has been provided, in a .csv file named: âPS3_NearshoreFishing.csvâ.
Description of variables:
HouseholdID: Unique identification number used to protect the identity of respondents
Poor: Indicates poor and non-poor households, as defined by the Indonesian National Poverty Line ($0.83 per capita per day).
Poor = 1 if household income is less than the INPL
= 0 if household income is more than the INPL
Quantity: The quantity of average harvest during one trip, in 10,000 Rp (currency)
For example, if average trip harvest is 2 kg of Grouper, and Grouper price is 20,000 Rp/kg, then Quantity of the trip is 40
Hours: The number of person hours spent fishing per trip, in hours.
For example, if average trip includes 3 fishermen, and each fishermen spends 3 hours fishing, then Hours of the trip is 9 person hours.
Capital: The value of capital used up during the average trip, in 10,000 Rp.
You can think of this like depreciation of all gear and boats used during a trip
Part 1:
(Model 1)
log(Quantityi)= b0 + b1log(Capitali) + b2log(Hoursi) + ei
1. Estimate the basic production model and report regression results. Include coefficients, standard errors, and t-statics. (Note: You will have to create new variables for estimation)
2. Based on your results, what is the marginal reurns to hours spent fishing? Be careful to interpret coefficient on log-transformed variables correctly.
3. Does the estimated production function have constant returns to scale, decreasing returns to scale, or increasing returns to scale? How do you know?
4. Using single hypothesis tests, which coefficients are significantly different than zero at a 5% significiance level?
5. Use Whiteâs Test to test for heteroskedasticity. Report results and evaluate the results.
Help with the following problems that deal with the program stata and with econometrics.
Below is the data needed.
HouseholdID | Poor | Quantity | Hours | Capital |
125465 | 0 | 25.4 | 8 | 0.796489877 |
130552 | 0 | 28.6 | 6 | 1.174603175 |
130552 | 0 | 9.1 | 4 | 2.222222222 |
127524 | 0 | 5 | 1 | 0.36544481 |
130538 | 1 | 10 | 6 | 2.008032129 |
130558 | 1 | 18.75 | 28 | 14.17848124 |
130462 | 1 | 14.4 | 2 | 0.487684729 |
126466 | 0 | 14.1 | 6 | 4.619435291 |
127474 | 1 | 13 | 3 | 0.367063492 |
127498 | 1 | 6 | 3 | 0.568124297 |
127471 | 0 | 12 | 5 | 0.115421137 |
127493 | 1 | 2.1 | 8 | 0.123444444 |
130561 | 0 | 39.6 | 3 | 0.289115646 |
130562 | 0 | 8 | 6 | 1.554278416 |
127532 | 1 | 41.7 | 6 | 0.738153469 |
127532 | 1 | 62.9 | 6 | 4.832562392 |
127495 | 0 | 7.65 | 3.5 | 0.116631206 |
127495 | 0 | 11.6 | 4 | 0.148772937 |
130524 | 1 | 2.95 | 10 | 0.706882255 |
130524 | 1 | 2.95 | 10 | 0.706882255 |
130564 | 0 | 14 | 14 | 1.495345632 |
127505 | 0 | 21.6 | 4 | 1.252053872 |
135460 | 1 | 21.5 | 4 | 0.757665094 |
131482 | 0 | 42.5 | 10 | 1.959625576 |
130560 | 0 | 15.3 | 4 | 0.697751323 |
128510 | 0 | 6 | 3 | 0.002311604 |
128510 | 0 | 4 | 2.5 | 0.416666667 |
128480 | 1 | 3.9 | 10 | 1.237449199 |
128480 | 1 | 4.4 | 10 | 1.237449199 |
128480 | 1 | 3.5 | 6 | 0.722079449 |
132456 | 0 | 8.5 | 5 | 0.177372685 |
132456 | 0 | 16.25 | 3 | 0.106423611 |
135486 | 0 | 21.5 | 11 | 3.665322581 |
135486 | 0 | 52.5 | 6 | 0.836021505 |
134524 | 0 | 33 | 7 | 1.242139722 |
135488 | 0 | 19.8 | 5 | 1.217105263 |
134460 | 0 | 84.4 | 3 | 3.824833703 |
131479 | 0 | 4 | 4.5 | 0.061111111 |
131465 | 0 | 8.5 | 1.5 | 0.39040198 |
128491 | 0 | 3.8 | 6 | 2.53815261 |
141514 | 1 | 1.4 | 6 | 0.946825397 |
134484 | 0 | 151.2 | 7 | 0.552428601 |
134484 | 0 | 71.2 | 6 | 0.479205754 |
141459 | 0 | 6.7 | 4 | 1.955605159 |
128473 | 0 | 70.7 | 5.5 | 0.553802416 |
128475 | 0 | 14.5 | 4 | 0.807217474 |
135520 | 0 | 2.5 | 4 | 1.041666667 |
135512 | 0 | 13.1 | 1 | 5.561594203 |
135512 | 0 | 3.3 | 2 | 0.650164062 |
134513 | 0 | 16.4 | 1 | 3.680053548 |
135469 | 1 | 18 | 13 | 1.979166667 |
132520 | 1 | 5.0625 | 2 | 0.395197395 |
134523 | 1 | 32.2 | 7 | 0.684749501 |
134497 | 0 | 10.76 | 5 | 3.18869165 |
129478 | 0 | 45.5 | 5.5 | 2.511574074 |
141461 | 0 | 25.6 | 2.5 | 4.849261849 |
141461 | 0 | 36.6 | 2.5 | 0.599912165 |
134503 | 0 | 30.6 | 8 | 1.214055483 |
128506 | 0 | 13.8 | 4 | 9.222222222 |
128506 | 0 | 19 | 4 | 9.222222222 |
130563 | 0 | 183.5 | 4 | 27.46449975 |
129488 | 0 | 215.1 | 1134 | 168.6111111 |
128487 | 0 | 4.5 | 1 | 0.000559284 |
129461 | 0 | 244 | 360 | 35.33333333 |
128496 | 0 | 1150 | 504 | 475.7380952 |
173468 | 0 | 2455 | 3366 | 1729.189322 |
134499 | 0 | 199 | 4 | 1.204772678 |
129466 | 0 | 4.5 | 3 | 2.773530545 |
145508 | 1 | 15 | 4 | 0.01460387 |
145508 | 1 | 15 | 4 | 0.01460387 |
134488 | 0 | 175 | 7 | 2.463414634 |
129484 | 0 | 275.1 | 2592 | 201.2685185 |
129484 | 0 | 175.1 | 1134 | 167.9891975 |
141467 | 0 | 16.5 | 2.5 | 0.270061728 |
141457 | 0 | 8.1 | 3 | 0.12021137 |
141457 | 0 | 24.1 | 4 | 0.499612792 |
135475 | 0 | 4.75 | 11 | 0.229402703 |
129498 | 0 | 616 | 830 | 362.7 |
134522 | 0 | 86.9 | 3 | 1.51324121 |
128477 | 0 | 9.4 | 5 | 1.626364087 |
141468 | 0 | 91.7 | 0.5 | 0.983115468 |
135489 | 1 | 18 | 8 | 3.206349206 |
134510 | 0 | 644.2 | 210 | 175.3837719 |
128457 | 0 | 3.5 | 2 | 0.509259259 |
134462 | 0 | 84.6 | 6 | 2.877641939 |
141509 | 1 | 23.2 | 2 | 2.640595716 |
129463 | 0 | 331 | 384 | 47.38180577 |
135514 | 1 | 18.6 | 2 | 8.338907469 |
135514 | 1 | 36.6 | 1 | 2.719893807 |
129485 | 0 | 4 | 7 | 0.833333333 |
129485 | 0 | 71.5 | 80 | 5.716746662 |
132529 | 1 | 7.8 | 3 | 1.024350649 |
132529 | 1 | 3.5 | 2 | 1.794733045 |
132529 | 1 | 1.5 | 3 | 0.861688312 |
145478 | 1 | 10.1 | 6 | 0.125 |
139510 | 1 | 12.5 | 10 | 6.041666667 |
134470 | 0 | 112 | 6 | 2.621527778 |
134496 | 0 | 279.7 | 4 | 4.799723021 |
134495 | 0 | 69 | 6 | 0.693735987 |
141460 | 0 | 60 | 2 | 1.272727273 |
135509 | 0 | 132.6 | 5 | 1.686077644 |
135506 | 0 | 10.5 | 3 | 0.295375197 |
134514 | 0 | 147.55 | 4 | 0.369502642 |
134514 | 0 | 147.55 | 4 | 0.369502642 |
134474 | 0 | 234.8 | 6 | 1.269918699 |
133503 | 0 | 6 | 3 | 1.095290252 |
133503 | 0 | 5.6 | 3 | 0.111111111 |
128460 | 0 | 15.5 | 5 | 0.306275676 |
128460 | 0 | 11.5 | 4 | 0.312922038 |
129501 | 0 | 500.5 | 483 | 74.36528749 |
129479 | 1 | 91 | 85 | 10.75104488 |
123490 | 1 | 15.75 | 5 | 1.35 |
123463 | 0 | 35.5 | 6 | 0.5 |
125465 | 0 | 18.5 | 6 | 0.568024685 |
127468 | 0 | 5.5 | 3.5 | 0.111111111 |
130552 | 0 | 13.1 | 2 | 1.166666667 |
130514 | 0 | 6.5 | 4 | 0.680555556 |
127524 | 0 | 14.5 | 5 | 2.532393505 |
130558 | 1 | 28 | 32 | 14.18542569 |
130516 | 0 | 3.5 | 4 | 0.208333333 |
130462 | 1 | 6.8 | 3 | 0.674055829 |
126466 | 0 | 12.6 | 2 | 4.592549518 |
127485 | 0 | 4.2 | 12 | 2.191666667 |
127485 | 0 | 10.2 | 6 | 1.186111111 |
130457 | 0 | 15 | 8 | 7.291666667 |
127474 | 1 | 10.5 | 3 | 0.724206349 |
127498 | 1 | 4.25 | 3 | 0.053412073 |
127498 | 1 | 3.5 | 3 | 0.053412073 |
127471 | 0 | 17.1 | 8 | 4.690142913 |
127471 | 0 | 12.3 | 4 | 2.311659648 |
127471 | 0 | 2.5 | 2 | 1.666666667 |
127493 | 1 | 2.1 | 8 | 0.123444444 |
130561 | 0 | 38.7 | 3 | 0.289115646 |
130561 | 0 | 16.5 | 3 | 11.33333333 |
127478 | 0 | 119.5 | 10 | 3.857877016 |
127478 | 0 | 30.5 | 6 | 2.170875421 |
127532 | 1 | 42.7 | 6 | 0.622768853 |
127532 | 1 | 38.7 | 6 | 6.971699297 |
127467 | 0 | 4.5 | 4 | 0.499600497 |
127467 | 0 | 9.1 | 3.5 | 0.366892361 |
127495 | 0 | 3.1 | 3.5 | 0.110797872 |
127495 | 0 | 9.9 | 3 | 0.114859845 |
130524 | 1 | 2.45 | 10 | 0.706882255 |
130524 | 1 | 2.45 | 10 | 0.706882255 |
130564 | 0 | 3814 | 3332 | 854.4818928 |
127505 | 0 | 14.5 | 3.5 | 2.491380471 |
135460 | 1 | 10 | 4 | 0.757665094 |
135460 | 1 | 20 | 14 | 0.484052111 |
131482 | 0 | 23.6 | 5 | 0.360957057 |
131482 | 0 | 67.9 | 6 | 0.416712483 |
130560 | 0 | 14 | 3 | 0.922110297 |
128510 | 0 | 504.6 | 1440 | 228.8873478 |
128510 | 0 | 6.3 | 2.5 | 0.416666667 |
128480 | 1 | 3.5 | 8 | 0.928789147 |
128480 | 1 | 49 | 70 | 33.6678911 |
132456 | 0 | 14.5 | 5 | 0.474991733 |
132456 | 0 | 8.75 | 5 | 0.177372685 |
132531 | 0 | 1.75 | 7 | 0.333333333 |
134524 | 0 | 33 | 7 | 1.116770991 |
134524 | 0 | 17 | 8 | 1.318727966 |
132513 | 0 | 1.5625 | 5 | 0.083333333 |
133494 | 0 | 2.875 | 2.5 | 0.5 |
135488 | 0 | 19.8 | 5 | 1.217105263 |
134460 | 0 | 40.8 | 3 | 3.824833703 |
128509 | 0 | 4216 | 2880 | 975.4285714 |
131479 | 0 | 2.35 | 4.5 | 0.42333225 |
131465 | 0 | 73 | 11.5 | 3.398356695 |
128491 | 0 | 6.4 | 3 | 1.871485944 |
141514 | 1 | 7.75 | 6 | 0.946825397 |
134484 | 0 | 91.7 | 7 | 0.962685011 |
134484 | 0 | 141.2 | 6 | 0.479205754 |
141459 | 0 | 12.2 | 4 | 1.955605159 |
128473 | 0 | 31.8 | 11 | 5.15297619 |
128481 | 0 | 852 | 810 | 49.09259259 |
128475 | 0 | 15.4 | 4 | 0.807217474 |
140461 | 1 | 4.7 | 5 | 1.183343855 |
128476 | 0 | 47 | 14 | 1.406476684 |
144544 | 0 | 21.2 | 2 | 0.866714015 |
135496 | 0 | 157.5 | 5 | 2.321399233 |
135496 | 0 | 59.8 | 5 | 2.003217415 |
134513 | 0 | 15.4 | 1 | 3.680053548 |
134523 | 1 | 28 | 40 | 3.667270345 |
144562 | 0 | 18.5 | 3 | 3.87254902 |
144562 | 0 | 11.4 | 3 | 2.086834734 |
134497 | 0 | 16.4 | 4 | 2.740795529 |
141461 | 0 | 34.1 | 2.5 | 4.849261849 |
141461 | 0 | 91.1 | 10 | 2.327184892 |
134503 | 0 | 29.6 | 8 | 1.214055483 |
128506 | 0 | 1271 | 1152 | 801 |
135497 | 0 | 0.75 | 1 | 0.221153846 |
141495 | 0 | 29 | 5 | 1.555555556 |
130563 | 0 | 252.5 | 8 | 36.62834591 |
141505 | 0 | 0.8 | 3 | 0.488855699 |
141505 | 0 | 0.8 | 3 | 0.513748468 |
133497 | 0 | 10 | 3 | 0.011904762 |
129488 | 0 | 210.5 | 1134 | 168.6111111 |
129461 | 0 | 722 | 720 | 70.66666667 |
128496 | 0 | 1150 | 504 | 475.7380952 |
173468 | 0 | 2882.5 | 1600 | 786.019471 |
145508 | 1 | 18.5 | 5 | 0.018254838 |
145508 | 1 | 16.65 | 5 | 0.018254838 |
134488 | 0 | 35 | 7 | 2.463414634 |
129484 | 0 | 371 | 2430 | 188.7268519 |
141467 | 0 | 25.65 | 2 | 1.158035714 |
141467 | 0 | 12.15 | 6.5 | 2.02808642 |
141457 | 0 | 19.8 | 3 | 0.167764213 |
141457 | 0 | 14.1 | 2 | 0.267971028 |
135475 | 0 | 5.75 | 10.5 | 0.22358875 |
129498 | 0 | 1068 | 830 | 362.7 |
134522 | 0 | 42.4 | 4 | 1.889213987 |
128477 | 0 | 7.6 | 6 | 1.919229497 |
144504 | 0 | 20.4 | 6 | 1.648461358 |
141468 | 0 | 35.65 | 0.5 | 0.983115468 |
135489 | 1 | 17.8 | 8 | 3.206349206 |
134510 | 0 | 384.7 | 90 | 75.16447368 |
128457 | 0 | 10 | 2 | 0.509259259 |
134462 | 0 | 114.6 | 7 | 2.918652438 |
141509 | 1 | 7.9 | 2 | 5.150635877 |
131485 | 0 | 6.75 | 8 | 2.973157134 |
131485 | 0 | 6.5 | 9 | 3.271105631 |
129463 | 0 | 1977.4 | 1848 | 224.9850657 |
135514 | 1 | 121.2 | 10 | 7.021349862 |
129485 | 0 | 1815 | 1296 | 80.22182224 |
132529 | 1 | 2.35 | 2.5 | 2.223124098 |
132529 | 1 | 7.6 | 2 | 1.875901876 |
132529 | 1 | 8.5 | 7 | 1.577705628 |
135502 | 0 | 31.2 | 4 | 0.320555556 |
132508 | 0 | 3.125 | 2.5 | 0.083333333 |
133479 | 0 | 26.7 | 2 | 4.126984127 |
134470 | 0 | 96 | 6 | 0.520833333 |
134496 | 0 | 114.8 | 7 | 2.416368587 |
134495 | 0 | 43 | 9 | 0.63703001 |
141460 | 0 | 23 | 2 | 1.272727273 |
132498 | 0 | 8 | 2 | 5.555555556 |
129497 | 0 | 2206 | 2880 | 955.3703704 |
129497 | 0 | 9.1 | 1.5 | 3.888888889 |
135509 | 0 | 2.6 | 5 | 0.942994199 |
135506 | 0 | 23.75 | 3 | 0.318339994 |
134514 | 0 | 37.55 | 7 | 0.596927834 |
134514 | 0 | 37.55 | 5 | 0.445311039 |
134474 | 0 | 114.75 | 6 | 1.269918699 |
133503 | 0 | 9 | 4 | 1.460387003 |
133503 | 0 | 6 | 3 | 0.111111111 |
128460 | 0 | 13.5 | 5 | 0.306275676 |
144502 | 0 | 6 | 3 | 0.644824673 |
129501 | 0 | 1280.2 | 672 | 123.9083139 |
129479 | 1 | 112 | 833 | 100.6137228 |
129511 | 0 | 231 | 60 | 0.02 |