Forecasting Sales Volumes

Question 1

What is time series analysis?

Answer 1

A mathematical technique for analyzing past observations to forecast future impacts.

Question 2

What are the four components of time series analysis?

Answer 2

• Long-term trend (T)
• Seasonal component (S)
• Cyclical variation (C)
• Random variation (R)

Question 3

What does the long-term trend (T) represent?

Answer 3

The underlying direction and quantity of change over the long term.

Question 4

What influences the long-term trend?

Answer 4

• Demographics
• Technological advancements
• Changes in lifestyles

Question 5

Define a linear trend.

Answer 5

A straight line trend represented by the equation T = a + bt.

Question 6

What is a logistic trend characterized by?

Answer 6

Slow growth followed by a spurt and then stagnation.

Question 7

What is an exponential trend and how is it represented?

Answer 7

A growth pattern like compound interest, represented by T = (1 + r)^t.

Question 8

Fill in the blank: Seasonal variations (S) are best described as _______.

Answer 8

[short-term trends and fluctuations due to seasonal circumstances]

Question 9

What are cyclical variations (C)?

Answer 9

Variations that occur over a longer period, often associated with economic cycles.

Question 10

True or False: Random variations (R) can be forecasted.

Answer 10

False

Question 11

What is the easiest method to identify a trend?

Answer 11

Plotting observations on a graph and drawing a ‘line of best fit’.

Question 12

What is an additive model in time series analysis?

Answer 12

Y = T + S + C + R, simplified to Y = T + S in exams.

Question 13

How is the seasonal variation calculated in an additive model?

Answer 13

S = Y - T.

Question 14

What does the multiplicative model represent?

Answer 14

Y = T x S x C x R, simplified to Y = T x S in exams.

Question 15

How is the seasonal variation calculated in a multiplicative model?

Answer 15

S = Y / T.

Question 16

Provide an example of seasonal variations.

Answer 16

• Higher sales of sun cream in summer
• Increased sales of scarves in winter
• Sales increases around holidays

Question 17

What is the equation for exponential growth?

Answer 17

T = (1 + r)^t.

Question 18

What is meant by adjusted values in time series analysis?

Answer 18

Forecasted figures that represent underlying trend values adjusted for seasonal variations.

Question 19

What is the definition of adjusted values in forecasting?

Answer 19

Adjusted values represent the underlying trend values, adjusted for any seasonal variation.

Question 20

In the equation y = 100 + 25x, what does ‘y’ represent?

Answer 20

Sales in units.

Question 21

In the equation y = 100 + 25x, what does ‘x’ represent?

Answer 21

The quarter number.

Question 22

How do you calculate the trend for a given quarter?

Answer 22

Set the x value equal to the quarter number and calculate the y value using the equation.

Question 23

What is the formula for additive seasonal variation?

Answer 23

S = Y - T, where Y is actual sales and T is trend sales.

Question 24

What is the additive variation for Quarter 1 if actual sales are 135 and the trend is 125?

Answer 24

10.

Question 25

What is the formula for multiplicative seasonal variation?

Answer 25

S = Y / T.

Question 26

What does a multiplicative seasonal variation of 1.08 indicate?

Answer 26

The number of units sold was 8% higher than the trend.

Question 27

What are the forecast sales for Quarter 5 using the additive model?

Answer 27

235 units.

Question 28

What are the forecast sales for Quarter 5 using the multiplicative model?

Answer 28

243 units.

Question 29

True or False: The additive model assumes seasonal variations remain constant over time.

Answer 29

True.

Question 30

True or False: The multiplicative model is generally considered superior to the additive model.

Answer 30

True.

Question 31

What is the formula for the trend line in linear regression?

Answer 31

T = a + bt.

Question 32

In the regression formula T = a + bt, what does 'a' represent?

Answer 32

The point at which the trend line intersects the vertical y-axis (at t = 0).

Question 33

In the regression formula T = a + bt, what does 'b' represent?

Answer 33

The increase (or decrease) in one time period.

Question 34

What does the symbol ∑ represent in regression analysis?

Answer 34

The 'sum of'.

Question 35

What is the least squares formula used for in linear regression?

Answer 35

To calculate the values of 'a' and 'b' for the trend line.

Question 36

What is the time period represented by 't' in the trend line formula?

Answer 36

The time period, starting from t = 1 for the first quarter.

Question 37

What is the trend forecast for Q2 of 20X4 if t = 18?

Answer 37

72.38.

Question 38

What would be the average of the y values (ȳ) if ∑y = 790.3 and n = 16?

Answer 38

49.39.

Question 39

What would be the average of the x values (x̄) if ∑x = 136 and n = 16?

Answer 39

8.5.

Question 40

What is the formula for calculating seasonal variation in the additive model?

Answer 40

Seasonal variation = Actual Value – Trend

Question 41

What is the formula for calculating seasonal variation in the multiplicative model?

Answer 41

Seasonal variation = Actual Value / Trend

Question 42

What are the average seasonal variations for each quarter?

Answer 42

* Q1: 0.83 * Q2: 1.00 * Q3: 0.96 * Q4: 1.21

Question 43

What is the formula for forecasted values using the multiplicative model?

Answer 43

Actual (forecasted) values (Y) = Trend (T) x Seasonal variation (S)

Question 44

What is the forecasted value for 20X4 Q1?

Answer 44

58.07

Question 45

What is the forecasted value for 20X4 Q2?

Answer 45

72.38

Question 46

What is the forecasted value for 20X4 Q3?

Answer 46

71.81

Question 47

What is the forecasted value for 20X4 Q4?

Answer 47

93.44

Question 48

What indicates a perfect correlation between two variables?

Answer 48

The line of best fit runs exactly through all of the points in the data set

Question 49

What indicates a partial correlation between two variables?

Answer 49

A generally increasing or decreasing trend with some variation

Question 50

What indicates no correlation between two variables?

Answer 50

No evidence of a relationship; points appear unrelated

Question 51

What is the correlation coefficient represented by?

Answer 51

r

Question 52

What does a correlation coefficient value close to 1 indicate?

Answer 52

A strong positive correlation

Question 53

What does a correlation coefficient value close to 0 indicate?

Answer 53

No correlation between the variables

Question 54

What does a correlation coefficient value close to -1 indicate?

Answer 54

A strong negative correlation

Question 55

How is the coefficient of determination calculated?

Answer 55

Coefficient of determination = r²

Question 56

What does a coefficient of determination of 0 indicate?

Answer 56

No relationship between changes in X and Y

Question 57

What does a coefficient of determination of 1 indicate?

Answer 57

Change in Y is solely due to change in X

Question 58

What is the rank correlation coefficient also known as?

Answer 58

Spearman's rank correlation coefficient

Question 59

What does the rank correlation coefficient measure?

Answer 59

The correlation between the rankings of two distributions

Question 60

What is the formula for calculating the rank correlation coefficient?

Answer 60

Rs = 1 - (6 ∑d²) / (n(n² - 1))

Question 61

What does a rank correlation coefficient close to 1 indicate?

Answer 61

A strong correlation between rankings

Question 62

What can be concluded from a rank correlation coefficient of 0.636?

Answer 62

There is some correlation between productivity and happiness, but it is low