Regression HW Solution

7/27/2019 Regression HW Solution

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SUMMARY OUTPUT

Regression Statistics

Multiple R 0.998281753

R Square 0.996566459

Adjusted R Square 0.995509984

Standard Error 1.001766854

Observations 18

ANOVA

df SS MS F Significance F

Regression 4 3786.523466 946.6309 943.2946 7.17946E-16

Residual 13 13.04597878 1.003537

Total 17 3799.569444

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 5.119473714 7.9069606 0.647464 0.5286 -11.9624761 22.20142353 -11.9624761 22.20142353

Px -0.32395922 0.155485138 -2.08354 0.057504 -0.659864438 0.011945999 -0.659864438 0.011945999 statistical sig

M 0.207662882 0.155759044 1.333232 0.205349 -0.128834074 0.544159839 -0.128834074 0.544159839 no significan

Py 0.248212681 0.23056592 1.076537 0.30126 -0.249894704 0.746320067 -0.249894704 0.746320067 no significan

Lagged Q 0.593553057 0.150835871 3.935092 0.001709 0.267691971 0.919414144 0.267691971 0.919414144 statistical sig

Qxt = 5.12 - 0.324 Pxt + 0.208 It + 0.248Pyt + 0.594 Qt-1 (0.65) (-2.08) (1.33) (1.08) (3.94)

Statistical significance of T-statistics is given by the P-values. There are three levels of significance: 1%, 5% and 10%.

Ignore the P-values given in this output because the sample period is very small. Instead, use the following standard significance levels

If t-statistics < 1.63 (plus or minus) then there is no statistical significance at any level.

If 1.63 < t-statistics < 1.96, there is statistical significance at the 10% level.

If 1.96 < t-statistics < 2.54, there is statistical significance at the 5% level

If t-statistics > 2.54, there is statistical significance at the 1% level.

CALCULATING ELASTICITIES FROM THE REGRESSION EQUATIONS

Short run price elasticity of demand = The slope of the price * (Average price / Average quantity)

= (-0.324*(11.84/25.19)) = -0.152

Long run price elasticity of demand = The slope of the price / [(1 - slope of lagged Q) * (Average price / Average quantity)]

= -0.152/(1-0.594)



= -0.374 [This is equivalent to dividing S/R elastcity over (1-slope of lagged Q)]

The Income elasticities can be estimated the same way.

Short run income elasticity of demand = The slope of income * (Average income / Average quantity)

= 0.208 * (20.39/ 25.189)

= 0.168

Income elasticity is positive and thus this good is a normal good. Since this elasticity is less than 1, this good is necessary in the short run.

Long run Income elasticity of demand can be rewritten as the ratio of the short run elasticity over (1 - the slope of lagged Q)

Long run Income elasticity of demand = 0.1684/(1-0.59355)

= 0.414

CROSS PRICE ELASTICITIES

Short run cross price elasticity of demand = The slope of the cross price * Average cross price / Average quantity

= 0.248*(24.61/25.19)

= 0.242

Long run cross price elasticity of demand = (The slope of the cross price) / [(1 - slope of lagged Q) * (Average cross price / Average quantity

= 0.2423/(1-0.594)

= 0.597

Question 3

The estimated equation is a demand equation. Thus we can add independent variables that are determinants of demand.

One of these determinant is the price of subsitiutes. We have Py as the price of one of the substitues. We can add another one if available.

That is, if this could be Raspberry, then prices of bluberries and strawberrys fit in here.

We can add the price of a components such as price of whipcream. We can add spending on advertising or taxes as independent variables.



Year Qx Px M Py Lagged Q

1984 4 30 5 15

1985 5 27 8 16 4

1986 5 26 8 18 5

1987 6 26 9 18 5

1988 7 25 10 19 6

1989 11 23 10 22 7

1990 13 20 11 24 11

1991 16 14 15 24 13

1992 21 11 15 25 16

1993 24 9 18 27 21

1994 28 7 20 27 24

1995 33 5 22 27.5 28

1996 36 4 25 27.5 33

1997 36.5 3.8 26 27.5 36

1998 39 3 30 27.5 36.5

1999 40 2.9 31 28 39

2000 42 2.4 33 28 40

2001 45 2.1 36 28.5 42

2002 46 2 40 28.5 45

Average 25.19 11.84 20.39 24.61

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Regression HW Solution