Discussion:
An investigator analysing the relationship between food expenditure, disposable income and prices in the US using annual data over the period 1959-83 computes the following regression
log(FOOD) = 4.7377 + 0.1069TIME + 0.3506log(PDI) - 0.5086log(PRICE)
(0.6805) (0.0033) (0.0899) (0.1010)
FOOD Total household expenditure on food
TIME A time trend
PDI Personal disposable income
PRICE The price of food deflated by a general price index
Figures in parentheses are standard errors
(i) Give an economic interpretation of the coefficients on log(PDI) and log(PRICE)
(ii) Test the hypothesis (using a 5% significance level) that the coefficient of log(PRICE) is equal to zero against the alternative that it is nonzero.
(iii) Test the hypothesis (using a 5% significance level) that the coefficient of log(INCOME) is equal to 1 against the alternative that is significantly different from 1.
You are now given the following extra information
SST = Σ(y_t - mean(Y))^2 = 0.53876
SSR = Σ(e_t)^2 = 0.0046276
(iv) Compute the SSE and R^2 for the above regression
(v) Test the joint hypothesis (at the 5% level) that the three 'slope' coefficients are all equal to zero against the alternative that at least one 'slope' coefficient is non-zero.