Year	Month	ChuckQ	ChuckP	PHQ	PHP	RibEQ	RibEP	ChickP	DiscInc	Trend
2001	1	120	$2.28	53	$6.04	74	$7.02	$1.61	8664.6	1
2001	2	76	$2.61	81	$5.37	79	$7.16	$1.68	8689.8	2
2001	3	102	$2.12	60	$5.74	71	$7.33	$1.57	8711.7	3
2001	4	106	$2.41	65	$6.93	112	$7.38	$1.73	8710.7	4
2001	5	87	$2.39	92	$5.95	113	$6.47	$1.74	8716.5	5
2001	6	94	$2.11	157	$5.24	89	$7.14	$1.63	8732.4	6
2001	7	97	$2.66	149	$5.39	146	$7.02	$1.69	8733.2	7
2001	8	79	$2.50	133	$5.54	120	$6.28	$1.71	8727.7	8
2001	9	138	$2.39	97	$6.28	120	$7.57	$1.79	8738.5	9
2001	10	129	$2.30	113	$5.43	106	$6.72	$1.65	8743.1	10
2001	11	77	$2.69	78	$5.46	76	$7.73	$1.75	8751.7	11
2001	12	94	$2.44	123	$4.81	93	$7.71	$1.79	8769.6	12
2002	1	135	$2.23	87	$5.49	83	$6.74	$1.65	8789.9	13
2002	2	120	$2.45	73	$5.54	136	$6.87	$1.72	8814.2	14
2002	3	131	$2.24	88	$5.76	119	$7.11	$1.68	8840.2	15
2002	4	104	$2.41	108	$5.28	114	$7.00	$1.67	8879	16
2002	5	144	$2.24	82	$6.05	151	$6.70	$1.63	8889.3	17
2002	6	139	$2.08	148	$5.34	248	$7.08	$1.66	8907.6	18
2002	7	98	$2.42	155	$5.10	201	$6.54	$1.73	8894.8	19
2002	8	112	$2.47	45	$6.88	168	$6.46	$1.73	8892.7	20
2002	9	184	$2.34	97	$5.67	165	$6.72	$1.76	8898.8	21
2002	10	98	$2.33	82	$5.65	105	$6.89	$1.68	8910.3	22
2002	11	109	$2.35	65	$6.38	88	$7.69	$1.62	8920.8	23
2002	12	135	$2.35	53	$6.22	108	$7.44	$1.83	8945.3	24
2003	1	132	$2.22	63	$5.86	182	$6.65	$1.70	8976.3	25
2003	2	142	$2.38	59	$6.72	150	$6.72	$1.67	9011.5	26
2003	3	128	$2.45	55	$7.12	144	$7.51	$1.68	9053.2	27
2003	4	94	$2.53	49	$6.54	121	$7.80	$1.84	9067.9	28
2003	5	93	$2.34	92	$6.70	161	$7.40	$1.81	9124.5	29
2003	6	126	$2.48	88	$6.91	280	$6.64	$1.74	9163.4	30
2003	7	83	$2.40	65	$7.33	170	$6.68	$1.71	9188.2	31
2003	8	109	$2.54	92	$6.70	165	$7.73	$1.82	9214.2	32
2003	9	112	$2.46	41	$7.75	106	$8.20	$1.80	9243.7	33
2003	10	83	$2.86	42	$7.22	104	$8.32	$1.80	9271.7	34
2003	11	90	$2.90	56	$7.57	91	$9.74	$1.79	9339.4	35
2003	12	77	$3.03	30	$8.40	63	$9.87	$1.85	9374.8	36
2004	1	86	$2.83	41	$6.65	67	$9.92	$1.61	9435.9	37
2004	2	165	$2.55	51	$6.94	111	$8.48	$1.61	9487.9	38
2004	3	109	$2.25	25	$7.40	118	$7.51	$1.64	9530.7	39
2004	4	89	$2.37	34	$7.45	107	$8.27	$1.66	9571.8	40
2004	5	125	$2.27	54	$7.51	125	$8.27	$1.66	9628.3	41
2004	6	108	$2.28	33	$8.60	117	$8.86	$1.66	9642.8	42
2004	7	88	$2.52	34	$8.54	119	$8.55	$1.70	9689	43
2004	8	101	$2.64	41	$8.36	143	$8.87	$1.85	9739.8	44
2004	9	85	$2.64	51	$6.98	100	$7.48	$1.72	9759	45
2004	10	113	$2.61	45	$6.88	82	$8.20	$1.63	9858.4	46
2004	11	85	$2.69	27	$7.19	73	$8.59	$1.68	9924.9	47
2004	12	90	$2.67	31	$7.08	70	$8.10	$1.64	10291	48
2005	1	113	$2.62	38	$6.89	89	$8.34	$1.59	10025.2	49
2005	2	98	$2.70	39	$7.05	84	$7.90	$1.55	10072.9	50
2005	3	86	$2.82	30	$7.80	105	$7.88	$1.61	10122	51
2005	4	93	$2.66	38	$7.88	111	$8.92	$1.64	10145.1	52
2005	5	127	$2.51	55	$7.68	159	$7.60	$1.60	10180.6	53
2005	6	83	$2.47	40	$8.17	141	$7.99	$1.65	10231.5	54
2005	7	94	$2.44	39	$8.06	156	$7.18	$1.62	10268.8	55

Variable definitions
ChuckQ	Quantity of Chuck Roast
ChuckP	Price of Chuck Roast ($/pound)
PHQ	Quantity of Porter House
PHP	Price of Porter House ($/pound)
RibEQ	Quantity of Ribeye
RibEP	Price of Ribeye ($/pound)
ChickP	Price of chicken ($/pound)
DiscInc	Disposable (after tax) income

Where is the beef?

The elasticity of demand is an important concept for business managers and policymakers to understand. It is not just a theoretical concept that you learn in textbooks, but rather has real-world practical applications. In this project, you are provided a dataset (Beef demand.xlsx ) that contains information on quantity and price of three cuts of beef (Chuck, Porter House, and Ribeye) plus data for chicken prices and disposable income of consumers, all on a monthly basis.

Estimate a linear multiple regression model of the three beef cuts. Use the estimated coefficients to calculate own-price, cross, and income elasticities of demand for each beef type. Fully interpret all regression results (coefficients) including t-ratios and p-values for statistical significance, R-squares, and F-statistics for testing the overall regression model fit. Present your regression results and all elasticity estimates and fully interpret their meanings. A log-linear model may also be used to estimate the elasticities directly.

Standard linear multiple regression model

Your multiple regression model should be of the form;

Qx = a + B₁X₁ + B₂X₂ + B₃X₃ + B₄X₄ + e_i

Q_x = an index of beef quantities for different cuts of beef (Chuck, Porter House, and Ribeye)

= constant (equals quantity of X when all other variables = 0)

X₁= the price of a given type of beef (Chuck, Porter House, Ribeye)

X₂= the price of a related good, chicken

X₃= measure of disposable (after-tax) income (DiscInc)

X₄ = trend variable (1,2,3.........n)

e_i =error term

Log-linear Model

Alternatively, you may specify a nonlinear demand function of the form;

Q_x = aP_x^B₁ P_c^B_zY^B_z Where: P_x = the price of a given type of beef

P_c = price of related good, chicken

Y = disposable income

By logarithmically transforming the above, you can then estimate the following log-linear equation:

log Qx= a + ₁ log Px + ₂ log Pc + ₃ log Y

where a = log

₁ = Own price elasticity

₂ = Cross-price elasticity

₃ = Income elasticity