How would I interpret these coefficient estimates?
The unknown equation of demand for beef is QDBeef= F (PBeef, PPork, PPotatoes, M)
A linear approximation to this unknown demand equation is
QDBeef= a - b PBeef cPPork dPPotatoese M
Where a, b, c, d and e are unknown parameters to be estimated using the data set and regression analysis.
According to your regression results, the estimated values of the unknown parameters are
a = 27001.460
b = -3237.903
c = 998.9908
d = - 2883.850
e = 0.41966
they are the coefficients associated toPBeef, PPork, PPotatoesand M.
QDBeef= 27001.460 - 3237.903 PBeef+ 998.9908PPork- 2883.850PPotatoes+ 0.41966 M
How can I best interpret this information for the coefficients?
Year Quantity Demanded of Beef (in million lbs) |Average Price of Beef per Ibs |Average Price of Pork per Ibs| Average price of Potato per Ibs Income Odb Pb Pp Po M SUMMARY OUTPUT 1980 24165.89 1.83 $ 1.46 $ 0.71 |$ 7,787.00 1981 24564.49 1.80 $ 1.67 $ 0.73 $ 8,476.00 Regression Statistics 1982 24810.86 1.77 $ 2.05 $ 0.71 $ 8,980.00 Multiple R 0.963400903 1983 25604.78 1.73 $ 1.94 $ 0.72 $ 9,494.00 R Square 1984 0.9281413 25849.62 1.72 $ 1.86 $ 0.81 $ 10,328.00 Adjusted R Square 1985 0.91886921 6271.84 1.68 $ 1.94 $ 0.76 $ 11,013.00 Standard Error 541.9372142 1986 26919.96 1.64 5 2.08 $ 0.84 $ 11,670.00 Observations 36 1987 26246.55 1.71 2.14 5 0.78 $ 12,391.00 1988 26354.57 1.76 $ 1.88 $ 0.85 $ 13,128.00 ANOVA 1989 25687.95 1.83 $ 0.93 $ 14,056.00 199 df SS MS 25433.99 F 1.97 $ Significance F 2.12 5 0.90 $ 14,387.00 199 Regression 117596496.8 25731.93 29399124.2 100.100545 2.90109E-17 1.97 $ 2.22 $ 0.88 $ 14,617.00 Residual 199 9104574.267 25945.14 293695.944 1.91 1.92 0.87 $ 14,847.00 Total 126701071.1 1993 25810.94 1.94 $ 1.93 $ 0.89 $ 15,777.00 1994 27286.94 1.86 $ $ 0.90 $ 16,555.00 Coefficients 1995 Standard Error t Stat 27873.74 P-value Lower 95% 1.84 $ Upper 95% Lower 95.0% Upper 95.0% 1.99 $ 0.92 $ 17,227.00 Intercept 27001.46068 780.5835829 1996 34.5913766 2.4768E-26 25409.44997 28116.18 1.80 $ 28593.4714 25409.44997 28593.4714 2.47 $ 0.97 $ 18,186.00 Beef -3237.90342 1997 450.5771251 -7.18612473 4.435E-08 28211.45 1.74 $ -4156.861525 -2318.945315 -4156.861525 -2318.945315 2.68 $ 1.00 $ 19,241.00 Pork 998.9908348 1998 376.9646833 28868.32 2.65009132 0.01255483 1.81 $ 230.1662944 1767.815375 230.1662944 1767.815375 2.54 $ 1.04 $ 20,120.00 Potatoes -2883.850406 1999 1734.072157 29759.18 1.84 $ -1.66305098 0.10638167 -6420.513888 652.8130758 -6420.513888 652.8130758 2.55 $ 1.06 |$ 21,239.00 Income 0.419066502 0.041607521 2000 10.071893 2.7001E-11 0.334207403 0.503925601 0.334207403 0.503925601 30331.63 1.94 $ 3.03 $ 1.07 $ 22,346.00 2001 29900.44 2.11 $ 3.25 $ 1.11 $ 22,851.00 2002 31015.6 2.13 $ 3.24 $ 1.07 $ 22,794.00 2003 30035.91 2.28 $ 3.20 $ 1.03 $ 23,276.00 2004 28847.23 2.50 $ 3.38 $ 1.07 $ 23,857.00 200 29022.31 2.54 $ 3.39 $ 1.06 $ 25,036.00 2006 29912.07 2.55 $ 3.44 $ 1.05 $ 26,352.00 2007 30205.36 2.70 $ 3.66 $ 1.12 $ 26,804.00 2008 29831.75 2.87 $ 3.66 $ 1.21 $ 26,964.00 00 29335.86 2.8 8 3.61 $ 1.28 $ 26,530.00 010 29274.52 2.91 $ 4.11 $ 1.26 $ 26,558.00 2011 28922.83 3.19 S 4.63 5 1.29 $ 27,554.00 2012 28815.34 3.41 $ 4.56 | $ 1.42 $ 28,281.00 2013 28648.24 3.47 $ 5.29 $ 1.50 $ 30,027.00 2014 27846.24 3.97 $ 5.78 $ 1.53 $ 30,176.00 2015 27721.26 4.25 $ 5.45 $ 1.49 $ 31,653.00