Regression Analysis

1. Qd=95.69- 0.41Beef price + 0 income* + 0.051 chicken price

2.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.988202765

R Square 0.976544704

Adjusted R Square 0.972146836

Standard Error 1.657790327

Observations 20

ANOVA

df SS MS F Significance F

Regression 3 1830.756 610.2519 222.0495705 3.02621E-13

Residual 16 43.9723 2.748269

Total 19 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 that