MA - Ch-12 = Forecasting Techniques

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?

A) A correlation coefficient numerically close to 1

B) Working to a higher number of decimal places of accuracy

C) Forecasting for values of X outside the range of those used in the sample

D) A large sample is used to calculate the regression equation

• A & B

• B & C

• A & D

• A & C

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?

A) High levels of car ownership cause high levels of road deaths

B) There is a strong relationship between the level of car ownership and the number of road deaths

C) 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

D) 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

• A & B

• B & C

• A & C

• B & d

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?

A) The estimate is not reliable because X is outside the range of the data

B) The estimate is not reliable because the correlation is low

C) The estimate is reliable

D) The estimate is not reliable because the sample is small

• A & D

• B & C

• A & C

• B & D

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