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Linear Regression Assignment

Linear Regression Assignment

Task I: Calculation of Linear Regression

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

priceX2a

.

Enter

a. All requested variables entered.

b. Dependent Variable: salesY

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.137a

.019

-.036

230.09712

a. Predictors: (Constant), priceX2

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

18120.198

1

18120.198

.342

.566a

Residual

953004.352

18

52944.686

Total

971124.550

19

a. Predictors: (Constant), priceX2

b. Dependent Variable: salesY

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

965.405

433.724

2.226

.039

priceX2

104.542

178.698

.137

.585

.566

a. Dependent Variable: salesY

y=965.405+104.542 x

x

y

1.8

1153.581

1.9

1164.035

2.1

1184.943

2.2

1195.397

2.2

1195.397

2.3

1205.852

2.4

1216.306

2.2

1195.397

2.3

1205.852

2.5

1226.76

2.5

1226.76

2.6

1237.214

2.7

1247.668

2.8

1258.123

2.9

1268.577

2.4

1216.306

2.4

1216.306

2.5

1226.76

2.7

1247.668

2.8

1258.123

Task II: Comments

From the above scatter plot and estimations in previous section, we can say see that the productions from our equation will not give a good forecast. In the scatter plot, the line of best fit cannot be said as the best estimator of the future trends.

Elasticity is the responsiveness to which one variable responds to a change in another variable Price elasticity of demand (PED) measures the responsiveness of quantity demanded of a product to a change in its price. If a relatively small change in price leads to a relatively large change in demand, the product is said to be 'elastic'.

Whereas if quantity demanded is relatively unresponsive to a change in price the product is said to be 'inelastic'.

Price elasticity of demand can be given a numerical value which is just a number and not in terms of any particular unit. The resulting numerical figure will always be a negative number due to the inverse relationship between price and quantity demanded, but can be ignored. This numerical figure can be calculated by: Price elasticity of demand = percentage change in quantity demanded Percentage change in price For example if the price of a product rises from £20 to £24, which is a 20%change and demand falls from 400 units to 300 units, which is a 25% change, the calculation will be:25% = -1.2520%When the percentage change in price leads to a smaller percentage change in quantity demanded price elasticity of demand will be a number between 0 and -1 and the product is said to be 'inelastic'.

On the other hand when the percentage change in price leads to a larger percentage change in quantity demanded price elasticity of demand will be a number between -1 and - infinity and the product is said to be 'elastic' such as the product used in the example above.

If the price elasticity of demand is exactly 1 the product is said to have 'unit' price elasticity of demand. This occurs when a percentage change in price leads to an equal percentage change in quantity demanded.

If a change in price causes an infinite change in quantity demanded the product is said to have 'perfectly elastic' demand. For example if there were a number of people selling football shirts outside a football stadium, if one of the sellers lowered their price below all of their competitors, they may capture all of the customers going to the stadium.

The final result is when a change in price causes no change to the quantity demanded and this is known as 'perfectly inelastic' demand. For example a person who has a serious illness and has to take drugs to survive may be prepared to purchase the same amount of ...

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