Supplementary Exercise 11.45 of IPS7e
-------------------------------------

A study on consumer ratings for a good-nutrition food product. A total of 162
consumers gave both an overall nutrition score and separate scores for different
parameters which later were averaged into two categories: favourable and
unfavourable. All scores were on a 9-point scale (high values correspond to good
to an evaluation as a healthy value).

The model fitted was a multiple linear regression model with two predictors, 
  Y_i = beta0 + beta1*Unfav_i + beta2*Favor_i + eps_i, i=1,...,162.

(a)
The least squares equation obtained was: y=3.96 + 0.86*Unfav + 0.66*Favor.


(b)
The entry "Model F" in the ANOVA table tests the hypothesis
  H0: all regression coefficients (excluding beta0) are zero,
      that is, beta1=0 and beta2=0
against the alternative hypothesis
  Ha: some of the regression coefficients are not zero,
      that is, either beta1<>0 or beta2<>0 or both.
The F-statistic follows an F(2,162-2-1=159) distribution, and the observed value
of 44.0 is indicated to have P<0.01. In fact, P<<0.001 so there is very strong
evidence against both of the predictors having no effect.


(c)
The t-statistics in the table test, for each of the three parameters beta0,
beta1 and beta2, the hypotheses H0: beta=0 against the alternative Ha: beta<>0.
The tests for the two predictors show that there is strong evidence for both
that the regression coefficient is non-zero. The test for the Constant
(intercept) tests the hypothesis that the expected value for a product with a
zero score on both predictors is zero. Most likely the value zero is not on the
scale of the predictors, so the hypothesis is of little interest. Anyway, this
t-test is strongly significant as well.


(d)
The t-statistics have 162-2-1=159 degrees of freedom.