Regression Analysis
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Qd=95.69- 0.41Beef price + 0 income* + 0.051 chicken price
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.988202765
R Square
0.976544704
Adjusted R Square
0.972146836
Standard Error
1.657790327
Observations
ANOVA
Significance F
Regression
1830.756
610.2519
222.0495705
3.02621E-13
Residual
43.9723
2.748269
Total
1874.728
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
95.6886488
2.537541
37.7092
4.63644E-17
90.30930209
101.068
90.3093
101.068
PrBeef
-0.408835674
0.05031
-8.12641
4.52214E-07
-0.515487065
-0.30218
-0.51549
-0.30218
Prof chicken
0.05101107
0.125871
0.405264
0.69065077
-0.21582407
0.317846
-0.21582
0.317846
Income
5.77987E-06
0.000748
0.007725
0.993931883
-0.001580336
0.001592
-0.00158
0.001592
*The 0 denotes a rounded figure of 5.77987E-06.
3. As in simple regression, the slope parameters b, c and d measure the change in Y associated with a one-unit change in one of the explanatory variables (in this case price of beef, income OR price of chicken), holding the rest of the explanatory variables constant. In the current equation, for example, a (price of beef) =0.41, then a ten-unit (in this case, the one-unit is 0.41) increase in Price of Beef results in a 4.1 increase in Y (the quantity of beef demanded), holding income and price of chicken constant.
4. The t-test is a statically test used to test the hypothesis that the true value of a parameter is equal to 0 (b=0). The test wills a lot the determination at statically how large b-hat must be in order to conclude that b is not equal to 0. T-ratio is the ratio estimated regression parameter divided by the standard error of the estimate. The numerical value of the t-ratio is the t-statistics. In order to prove, that the current equation cannot be rejected, we have to determine the t-statistics to be larger than the critical value of t (2.12 at 16 [20-4] degree of freedom, 0.05 level of significance). Since each dependant variable, PrBeef(-8.13), Prof chicken (0.41) and Income (0.01) are les than the critical value of t. It can be said that the parameters should be rejected. The hypothesis will not be accepted.
The p-value used in hypothesis tests to help you decide whether to reject or fail to reject a null hypothesis. The p-value is the probability of obtaining a test statistic