Regression analysis is being used to fine the line of best fit (y = a + bx) from eleven pairs of data. The calculations have produced the following information:

Σx = 440, Σy = 330, Σx² = 17,986, Σy² = 10,366 and Σxy = 13,467

What is the value of 'a' in the equation for the line of best fit? (to 2 decimal places)

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?

What is the purpose of seasonally adjusting the values in a time series?

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?

The following information is available for the price of materials used at P Co.

What is Fisher's ideal index?

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?

Which TWO of the following are necessary if forecasts obtained from a time series analysis are to be reliable?

Unemployment numbers actually recorded in a town for the second quarter of the year 2000 were 4,700. The underlying trend at this point was 4,300 people and the seasonal factor is 0.92. Using the multiplicative model for seasonal adjustment, what is the seasonally-adjusted figure (in whole numbers) for the quarter?

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?

A company uses regression analysis to establish a total cost equation for budgeting purposes.

Data for the past four months is as follows:

The gradient of the regression line is 17.14.

What is the value of a?

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?

A spreadsheet is unlikely to be used for which of the following tasks?

A large bag of cement cost $0.80 in 20X3. The price indices are as follows.

How much does a bag of cement cost in 20X6 (to 2 dp)?

The following statements relate to Paasche and Laspeyre indices.

1. Constructing a Paasche index is generally more costly than a Laspeyre index
2. With a Laspeyre index, comparisons can only be drawn directly between the current year and the base year

Which statements are True?

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?

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?

The following question is taken from the June 2013 exam.

An additive time series has the following trend and seasonal variations:

Trend           Y=4,000 + 6X

where           Y= sales in units

X is the number of quarters, with the first quarter of 2014 being 1, the second quarter of 2014 being 2 etc.

Seasonal variation

What is the forecast sales volume for the fourth quarter of 2015?

If Σx = 12, Σy = 42, Σx² = 46, Σy² = 542, Σxy = 157 and n = 4, what is the correlation coefficient?

Which of the following is a feasible value for the correlation coefficient?

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?

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?

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.)

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?

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?

Which of the following are common applications of spreadsheets used by management accountants?

1. Variance analysis
2. Cash flow budgeting and forecasting
3. Preparation of financial accounts

The following spreadsheet shows part of a time series analysis of a company’s sales.

What is the four quarter centred moving average of sales units for quarter 4, 2014?

The following information relates to a company’s semi-variable production overheads.

What is the variable overhead cost per unit, expressed in 2013 prices?

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?

Which TWO of the following are necessary if forecasts obtained from a time series analysis are to be reliable?

The following data relates to a company's overhead cost.

Using the high low technique, what is the variable cost per unit (to the nearest $0.01) expressed in current year prices?

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)

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?

Under which of the following circumstances would a multiplicative model be preferred to an additive model in time series analysis?

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?