EC255 Lecture 3: Lecture #3

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salmonreindeer280

17 Sep 2017

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Ec255 lecture #3: descriptive statistics (continued) & probability. Measures of variability ungrouped data: used to indicate how much are the observations spread out around the mean, common measures range, mean absolute deviation, variance, standard deviation, coefficient of variation, difference between the largest and smallest values. Range: (cid:1870)(cid:1866)(cid:1859)(cid:1857)=(cid:3040)(cid:3040)(cid:3040) (cid:3040)(cid:3041)(cid:3040)(cid:3040) ignores all other data points ignores the way data is distributed, simple to compute, sensitive to outliers. Mean absolute deviation: average of the absolute deviations from the mean (no negative numbers, (cid:1830)= | | =(cid:2870)(cid:2872)(cid:2873)=(cid:886). (cid:890) x x . Population variance: average of the squares of deviations from the mean, (cid:2870)= (cid:4666) (cid:4667)2 =(cid:2869)(cid:2871)(cid:2868)(cid:2873) =(cid:884)(cid:888, computational formula: (cid:2870)= 2 (cid:4666) (cid:4667)2. Interpreting standard deviation: supposed that the mean and standard deviation of last year"s final exam are 70 and 5, respectively if the histogram is bell shaped, approx. 68% of the marks were between 65 and 75 (1 stdev [5x1=5 from the avg]: approx.

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PROBLEM SET ONE -2 - PRICE-ELASTICITY OF DEMAND

	P₁	P₂	Q_D1	Q_D2	I	II	III	IV	V
1	1	2	10	5
2	5	3	40	90
3	12	20	200	200
4	3	2	9	9
5	0.40	1.40	30	15
6	1.2	4.0	20	15
7	7.5	4.6	40	30
8	5	5.000â¦01	1x10⁶	0
9	5	4.9999â¦.	10	1x10⁹
10	6	12	12	6
11	18	36	360	180
12	7	15	24	16
13	7	16	78	78
14	25	65	150	100
15	65	91	1300	780
16	4	5	21	11
17	8	4	30	54
18	140	275	625	495
19	78	91	780	780
20	91	78	780	780

Column I - determine the Price-Elasticity of Demand Coefficient. Find material in Chapter 6 and the Powerpoint of Elasticity Chap 004 19e.ppt

change in quantity demanded change in price

E_D = ---------------------------------------- â ----------------------------

sum of quantities demanded / 2 sum of prices / 2

The data in the first four columns represent price (P) and quantity demanded (Qd) in time 1 (before change in price) and time 2 (after change in price). Note that results should be expressed in absolute terms (see paragraph Elimination of Minus Sign). For example, -1 should be expressed as â1â.

Column II â Based on topic concerning Interpretations of E_D, indicate which applies based on how the quantity demanded changed subsequent to a change in price (elastic, inelastic, etc.)

Column III - you need to determine if the good in question would be considered a necessity, a luxury or neither.

Column IV â Indicate, in monetary terms, how much is the change in total revenue or total expenditure (TR = P X Q_D), from the first price level to the second.

Column V - the direction of the change, also in monetary terms, that is, increasing or decreasing, and by how much? (show a + sign for increasing and a â sign for decreasing).

Note: for any monetary result please include the applicable currency symbol ($, â¬, etc.)

salmoneagle868

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

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12^th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12^th 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.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3^rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

	A	B	C	D	E
1
2
3	Date	Price of gas
4	Jan 07, 2008	325.3
5	Jan 14, 2008	323.9
6	Jan 21, 2008	320.1
7	Jan 28, 2008	316.3
8	Feb 04, 2008	313.5
9	Feb 11, 2008	310.7
10	Feb 18, 2008	315.4
11	Feb 25, 2008	324.6
12	Mar 03, 2008	325.2
13	Mar 10, 2008	326.3
14	Mar 17, 2008	333.7
15	Mar 24, 2008	332.1
16	Mar 31, 2008	334.8
17	Apr 07, 2008	336.6
18	Apr 14, 2008	341.6
19	Apr 21, 2008	355
20	Apr 28, 2008	366.9
21	May 05, 2008	367.7
22	May 12, 2008	376.4
23	May 19, 2008	384.9
24	May 26, 2008	397.5
25	Jun 02, 2008	402.6
26	Jun 09, 2008	407
27	Jun 16, 2008	411.8
28	Jun 23, 2008	411
29	Jun 30, 2008	411.3
30	Jul 07, 2008	412.3
31	Jul 14, 2008	411.7
32	Jul 21, 2008	408.4
33	Jul 28, 2008	400.2
34	Aug 04, 2008	393.9
35	Aug 11, 2008	386.6
36	Aug 18, 2008	376.4
37	Aug 25, 2008	371.5
38	Sep 01, 2008	369.8
39	Sep 08, 2008	367.1
40	Sep 15, 2008	373
41	Sep 22, 2008	368
42	Sep 29, 2008	362.7
43	Oct 06, 2008	351.7
44	Oct 13, 2008	323.9
45	Oct 20, 2008	305
46	Oct 27, 2008	286.1
47	Nov 03, 2008	265.4
48	Nov 10, 2008	247.7
49	Nov 17, 2008	229.4
50	Nov 24, 2008	212.8
51	Dec 01, 2008	203
52	Dec 08, 2008	191.8
53	Dec 15, 2008	181
54	Dec 22, 2008	178.1
55	Dec 29, 2008	174.1

QUESTION 13

Label the next column (D) "6-month change." Here we will calculate how much prices have changed since the price six months ago. For example, if the price on January 1 were 224.1 and the price on July 1 is 324.1, the price change is 100. We can't calculate how much prices have changed over the past six months for the first half of 2008 because we don't know the price six months before. So, in column D, put an x in each cell for which we can't calculate the 6-month change. Starting in July, we can calculate the 6-month change. Using cell references, enter here the formula you should enter into cell D30 to calculate the 6-month change.

2 points

QUESTION 14

Copy and paste the formula from cell D30 (from the last question) into cells D31 to D55. What formula is now in cell D48?

2 points

QUESTION 15

What value is now in cell D50?

1 point

QUESTION 16

Label the next column (E) "% of Jan." In this column, we will divide every week's price by the price from January 7th. This will tell us as a percent how prices compare to their level at the start of the year. This time, we want an "absolute" reference so that it doesn't consider the position (i.e. "8 to the left and 2 down") but just locks in on B4 every time. To set up an absolute reference in a formula, we put the $ character into the reference, so instead of B4, we use $B$4. With the dollar signs in place, you can copy the formula and paste it, and in each case, it will go back to B4 regardless of where you are when you paste it. What formula should you type into cell E5 to get the "% of Jan" for January 14, 2008? Remember to use the absolute reference so it will be easy to copy later!

2 points

QUESTION 17

Copy and paste the formula from cell E5 into the rest of column E. (Well, at least from E6 down to E55.) What formula is now in cell E17?

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EC255 Lecture 3: Lecture #3

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