WorksheetsMA - Ch-12 - Forecasting Techniques
Total questions: 25
Worksheet time: 34mins
The following four data pairs have been obtained: (1, 5), (2, 6), (4, 9), (5, 11).
Without carrying out any calculations, which of the following correlation coefficients best describes the relationship between x and y?
–0.98
–0.25
0.98
0.25
A company's management accountant is analysing the reject rates achieved by 100 factory operatives working in identical conditions. Reject rates, Y%, are found to be related to months of experience, X, by this regression equation: Y = 20 – 0.25X. (The correlation coefficient was r = –0.9.)
Using the equation, what is the predicted reject rate for an operative with 12 months' experience?
17%
19%
20%
23%
A regression equation Y = a + bX is used to forecast the value of Y for a given value of X.
Which TWO of the following increase the reliability of the forecast?
1. A correlation coefficient numerically close to 1
2. Working to a higher number of decimal places of accuracy
3. Forecasting for values of X outside the range of those used in the sample
4. A large sample is used to calculate the regression equation
1 & 4
1 & 3
2 & 4
2 & 3
If x = 12, y = 42, x2 = 46, y2 = 542, xy = 157 and n = 4, what is the correlation coefficient?
0.98
–0.98
0.26
0.008
Using data from twelve European countries, it has been calculated that the correlation between the level of car ownership and the number of road deaths is 0.73.
Which TWO of the statements shown follow from this?
1. High levels of car ownership cause high levels of road deaths
2. There is a strong relationship between the level of car ownership and the number of road deaths
3. 53% of the variation in the level of road deaths from one country to the next can be explained by the corresponding variation in the level of car ownership
4. 73% of the variation in the level of road deaths from one country to the next can be explained by the corresponding variation in the level of car ownership
1 & 2
2 & 4
1 & 3
1 & 4
The regression equation Y = 3 + 2X has been calculated from 6 pairs of values, with X ranging from 1 to 10. The correlation coefficient is 0.8. It is estimated that Y = 43 when X = 20.
Which TWO of the following are true?
1. The estimate is not reliable because X is outside the range of the data
2. The estimate is not reliable because the correlation is low
3. The estimate is reliable
4. The estimate is not reliable because the sample is small
1 & 4
2 & 3
2 & 4
1 & 3
In calculating the regression equation linking two variables, the standard formulae for the regression coefficients are given in terms of X and Y.
Which of the following is true?
X must be the variable which will be forecast
It does not matter which variable is which
Y must be the dependent variable
Y must be the variable shown on the vertical axis of a scatter diagram
A company uses regression analysis to establish a total cost equation for budgeting purposes.
The gradient of the regression line is 17.14.
What is the value of a?
25.36
48.56
74.64
101.45
Which of the following is a feasible value for the correlation coefficient?
- 2.0
- 1.2
0
+ 1.2
Over an 18-month period, sales have been found to have an underlying linear trend of y = 7.112 + 3.949x, where y is the number of items sold and x represents the month. Monthly deviations from trend have been calculated and month 19 is expected to be 1.12 times the trend value.
What is the forecast number of items to be sold in month 19?
91
92
93
94
Based on the last 15 periods the underlying trend of sales is y = 345.12 – 1.35x. If the 16th period has a seasonal factor of –23.62, assuming an additive forecasting model, what is the forecast for that period, in whole units?
300
301
324
325
Monthly sales have been found to follow a linear trend of y = 9.82 + 4.372x, where y is the number of items sold and x is the number of the month. Monthly deviations from the trend have been calculated and follow an additive model. In month 24, the seasonal variation is estimated to be plus 8.5.
What is the forecast number of items to be sold in month 24? (to the nearest whole number.)
106
115
123
152
What is the purpose of seasonally adjusting the values in a time series?
To obtain an instant estimate of the degree of seasonal variation
To obtain an instant estimate of the trend
To ensure that seasonal components total zero
To take the first step in a time series analysis of the data
The following data represents a time series:
X 36 Y 41 34 38 42
A series of three point moving averages produced from this data has given the first two values as 38 and 39.
What are the values of (X, Y) in the original time series?
(38, 39)
(38, 40)
(40, 38)
(39, 38)
Using an additive time series model, the quarterly trend (Y) is given by Y = 65 + 7t, where t is the quarter (starting with t = 1 in the first quarter of 20X5). If the seasonal component in the fourth quarter is –30, what is the forecast for the actual value for the fourth quarter of 20X6, to the nearest whole number?
63
546
85
91
The trend for monthly sales ($Y) is related to the month (t) by the equation Y = 1,500 – 3t where t = 1 in the first month of 20X8. What are the forecast sales (to the nearest dollar) for the first month of 20X9 if the seasonal component for that month is 0.92 using a multiplicative model?
$1,377
$17,904
$1,344
$1,462
Under which of the following circumstances would a multiplicative model be preferred to an additive model in time series analysis?
When a model easily understood by non-accountants is required
When the trend is increasing or decreasing
When the trend is steady
When accurate forecasts are required
A company's annual profits have a trend line given by Y = 20t – 10, where Y is the trend in $'000 and t is the year with t = 0 in 20X0.
What are the forecast profits for the year 20X9 using an additive model if the cyclical component for that year is –30?
$160,000
$140,000
$119,000
$60,000
In January, the unemployment in Ruritania is 567,800. If the seasonal factor using an additive time series model is +90,100, what is the seasonally-adjusted level of unemployment (to the nearest whole number)?
90,100
477,700
567,800
657,900
The following statements relate to Paasche and Laspeyre indices.
(i) Constructing a Paasche index is generally more costly than a Laspeyre index
(ii) With a Laspeyre index, comparisons can only be drawn directly between the current year and the base year
Which statements are true?
Both statements are true
Both statements are false
(i) is true and (ii) is false
(ii) is true and (i) is false
The following information is available for the price of materials used at P Co. Laspeyre index for price in 20X5 (with base year of 20X0) 150.0
Corresponding Paasche index 138.24
What is Fisher's ideal index?
12.00
16.98
144.00
288.24
7 Four years ago material X cost $5 per kg and the price index most appropriate to the cost of material X stood at 150.
The same index now stands at 430.
What is the best estimate of the current cost of material X per kg?
$1.74
$9.33
$14.33
$21.50
8 Six years ago material M cost $10 per kg and the price index most appropriate to the cost of material M was 130. The same index now stands at 510.
What is the best estimate of the current cost of material M per kg?
$2.55
$29.23
$39.23
$51.00
Which of the following are common applications of spreadsheets used by management accountants?
(i) Variance analysis
(ii) Cash flow budgeting and forecasting
(iii) Preparation of financial accounts
(i) and (ii) only
(i) and (iii) only
(ii) and (iii) only
(i), (ii) and (iii)
A spreadsheet is unlikely to be used for which of the following tasks?
Cash flow forecasting
Monthly sales analysis by market
Writing a memo
Calculation of depreciation
