Calculation of Coefficient of Concurrent Deviations

The coefficient of concurrent deviations measures the degree to which two variables move together over time. It is a measure of the strength of the relationship between two variables. In this case, we are interested in the relationship between price and demand.

Step 1: Calculate the mean of the price and demand data.

- Mean of Price = (35 + 38 + 40 + 33 + 45 + 48 + 49 + 52) / 8 = 42.5
- Mean of Demand = (36 + 35 + 31 + 36 + 30 + 29 + 27 + 24) / 8 = 31.5

Step 2: Calculate the deviations from the mean for each year.

- Deviation from Mean of Price = Price - Mean of Price
- Deviation from Mean of Demand = Demand - Mean of Demand

Year Price Deviation from Mean of Price Demand Deviation from Mean of Demand

1996 35 -7.5 36 4.5
1997 38 -4.5 35 3.5
1998 40 -2.5 31 -0.5
1999 33 -9.5 36 4.5
2000 45 2.5 30 -1.5
2001 48 5.5 29 -2.5
2002 49 6.5 27 -4.5
2003 52 9.5 24 -7.5

Step 3: Calculate the product of the deviations for each year.

- Product of Deviations = Deviation from Mean of Price * Deviation from Mean of Demand

Year Price Deviation from Mean of Price Demand Deviation from Mean of Demand Product of Deviations

1996 35 -7.5 36 4.5 -33.75
1997 38 -4.5 35 3.5 -15.75
1998 40 -2.5 31 -0.5 1.25
1999 33 -9.5 36 4.5 -42.75
2000 45 2.5 30 -1.5 -3.75
2001 48 5.5 29 -2.5 -13.75
2002 49 6.5 27 -4.5 -29.25
2003 52 9.5 24 -7.5 -71.25

Step 4: Calculate the sum of the products of deviations.

- Sum of Products of Deviations = Σ(Product of Deviations)

Sum of Products of Deviations = -207.75

Step 5: Calculate the sum of the squared deviations for each variable.

- Sum of Squared Deviations of Price = Σ(Price - Mean of Price)^2
- Sum of Squared Deviations of Demand = Σ(Demand - Mean of Demand)^2

Year Price Deviation from Mean of Price (Price - Mean of Price)^2 Demand Deviation from Mean of Demand (Demand - Mean of Demand)^2

1996 35 -7.5 56.25 36 4.5 20.25
1997 38 -4.5 20.25 35 3.5