UNI101Y1 Lecture : Ch11 Population Growth and Regulation2.pdf

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burgundydog64

16 Feb 2013

School

UTSG

Department

University College Courses

Course

UNI101Y1

Professor

Spencer Barrett

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Document Summary

The rate of geometric growth is most conveniently expressed as a ratio of a pop. "s size in one year to its size in the preceding year (or other time interval) Never a ve # of indiv. , thus is always +ve. Geometric growth has the equation as eexxppoonneennttiiaall ggrroowwtthh n(t) = n(0)ert. Variable r is the exponential growth rate. Constant e is the base of natural logarithms (~2. 72) Geometric and exponential growth are related by = er and loge = r. When a pop. undergoes geometric growth at a constant rate, the # of indiv. added to or removed from the pop. varies w/ the size of the pop. Change in pop. size from one time period to the next is n. Change over one interval is the diff. b/w the pop. size at the beginning and at the end of the interval. When > 1, + n, pop. grows. When < 1, - n, pop. declines.

Related Questions

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

PLEASE ANSWER ALL QUESTIONS OR DO NOT ANSWER.

1. The formula

A = P[1 + (r/n)]^nt

describes the accumulated value A of a sum of money P, the principal, after t years at annual percentage rate r (in decimal form) compounded n times a year. How long will it take $25,000 to grow to $500,000 at 9% annual interest compounded monthly

Also:

Solve the logarithmic equation algebraically: Ln (X+5) = Ln (Xâ1) â Ln (X+1)

2. What is the first derivative of the following:

f(x) = ln (2x / x+1)

it is Natural Log of 2x over x+1

3. Please read the article from Money Magazine, posted in our week 8 Module, (one of my favorite financial magazines) that talks about small drop in t-bills will result in a major return in your investments (second paragraph). Why do you think that is? The article is a bit old but the question here is quite relevant about what we cover this week.

Hint: It has to do with the exponential graphs.

ARTICLE: Photo provided

THE ECONOMY: "Though growth averaged 2.5% stock market. says Leuthold, who recently completed a study of the stock market's daily ns over the past 100 years. In fact the stock market's daily swings from 1992 through '95 were less than half the historical average. Recently, however, daily fluctuations BY MICHAEL SIVY prices have cruised frm one high tothe next the stock market's daily swings from 1992 MosT OF THE PAST FOUR YEARS. STOCK ups and dow from one high to the next h, silent ride of a Rolls-Royce. But since March, the market has been lurching at an annual rate invest additional cash in stocks when they're low. If volatili in the first half of oyour Donailene tem dieapsirm ke a broken-down jalopy If you're hesitant to in stock prices have doubled (see the chart be- n't worry. Consider putting some be a sign that we're getting close to a market so jumpy. do of your money in long-term bonds instead. close to a mak t 1996, it will slow likely to beat stocks over the This short-term forecast doesn't change presi- the fact that the five-year outlook for stocks is terrific-thanks to the enormous underlying JTTERY AGAIN Percentage of trading days strength of the U.S. econ- the Dow moved more than 1% omy and the fact that aging -Bonds are next 12 months, says Steve Leuthold, dent of the Leuthold Group. STOCK PRICES ARE GETTING later this year.â nnpolis cuipd AGAIN advisory firm. We couldn't agree more. In fact, the out look for long-term bonds is the best it's been for more omy and the fact that agi baby boomers are continu- ing to sock away more than S20 billion a month in "The Dow couldthan a year. reach 6000 by fall but wil Here's our analysis: We see the economy slowing from its current 2.5% growth rate to only 2% or so late this year. Furthermore, stock mutual funds. Nonetheless, this is atime to restrict any new invest- ments in stocks to conserva- it makes sense to favor issues that are likely to boost their dividends, such as the shares decline ofas much as 15% starting beforea result, long-term-bond year-end." yields could sink from to day's 69% to as low as 6% by year-end. That rate decline would produce total re turns the Wall Street Newsletter n page 58. Stocks with solid around less than growth on bonds and other Income investments could return uping to fall s to 20% in the coming year. Moreover, as you sell By contrast, stocks increasingly look as some of your past year's winners, don't feel hough they are poised for a temporary 15% you have to reinvest all your profits in stocks. Consider putting some money into are likely to 30-year Treasuries (and mutual funds that start worrying that corporate profits are go- hold such long-term. high-quality issues). In hort of analysts' estimates and short, fortify your asset mix with bigger mark down share prices. "Slower earnings holdings of long-term bonds and other in- gains could turn the stock market's ail come investments such as high-yield stocks. portfo- drop in the second half of 1996. Reason: As the economy siows, investors winds into head winds." says economist That will help you keep your overall Michael SivyKathryn J. Lunstrum at Duff & Phelps in lio on track to a double-digit return even if the stock market takes a nasty 15% tumble in The tip-off that a stock market pullback the coming year. may be close is the increasing volatility o share prices over the past three months. Wall Street editor Michad Sivy is a chartered fi Volatility tends to be low in a strong, rising analyst and a former Wall Street researth director. nancia

UNI101Y1 Lecture : Ch11 Population Growth and Regulation2.pdf

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