Reference no: EM131994
(1) (i) Using Excel, estimate using regression analysis the linear demand equation of Q_{x} on P_{x}, P_{y}, Advertising and Income. Write down this estimated equation.
(ii) Consider that in 2012 P_{x}, P_{y}, Advertising and Income are all 10% greater than their 2011 value._{ }Using the estimated equation in the previous part, calculate all the point elasticities of demand (income, price, cross price, and advertising elasticities) in Year 2012. Comment on your results (e.g. is demand for X elastic or inelastic; are X and Y substitutes or complements; is X a normal or an inferior good; is X a luxury or a necessity; is X sensitive to advertising or not).
(iii) Describe how a business may utilize these elasticities to inform its decisionmaking process.
(2) (i) Using Excel, transform all variables into natural logarithms (ln). Then use these variables to evaluate the demand equation in loglinear form (i.e. ln(Q_{x}) on ln(P_{x}), ln(P_{y}), ln(Income) and ln(Advertising). Write down this estimated equation.
(ii) Based on the evaluated loglinear model, what are the elasticities of demand ( income, price, cross price, and advertising elasticities)? Do the conclusions you have reached in Part 1(ii) still hold?
(3) (i) For each model (loglinear and linear model), investigate which of the explanatory variables are individually statistically significant at the 5% significance level.
(ii) Conduct an Ftest (at the 1% significance level) for each model and comment on the results.
(iii) Based on economic theory and the statistical tests you have conducted, which model do you consider preferable (the linear or loglinear model)?
The following table provides information on the quantity demanded of commodity X (Q_{x}), its price (P_{x}), and the price of related good Y (P_{y}) from 1980 to 2011.

Qx

Px

Py

Income

Advertising

1980

120.5

280

230

53801.16

100

1981

140.2

240

250

56437.504

120

1982

135.1

265

240

57755.075

115

1983

163.7

250

250

59736.251

140

1984

142.4

240

240

61765.159

125

1985

131.6

270

245

63422.59

111

1986

180.8

240

220

66091.16

160

1987

201.7

215

280

70092.659

180

1988

164.8

250

276

77764.084

141

1989

133.6

265

250

75205.738

113

1990

137.8

265

249

68348.947

116

1991

183.3

240

240

62576.636

165

1992

211.7

230

240

58038.468

200

1993

237.5

225

234

57179.301

270

1994

209.5

225

250

58218.893

195

1995

196.8

220

235

59884.088

175

1996

159.5

230

240

54256.702

135

1997

183.2

235

250

51231.436

164

1998

190.5

245

249

53284.208

170

1999

205.5

240

240

54510.731

185

2000

175.7

250

289

57631.999

150

2001

191.6

240

230

60024.551

174

2002

212.7

240

250

62815.812

205

2003

202.2

235

240

66274.054

190

2004

220.8

220

231

70746.422

240

2005

221.2

218.7

239

75244.697

243

2006

223.9

220

257

80143.598

245

2007

225.1

219

236

85311.444

246

2008

229

216.5

230

90592.766

255

2009

231.9

215.6

230

85631.577

260

2010

233

213

256

85967.913

265

2011

234.5

212.5

245

87402.494

270
