In the linear consumption function

dcons = ^ 0 + ^ 1inc;

the (estimated) marginal propensity to consume (MPC) out of income is simply the slope, ^ 1, while the average

propensity to consume (APC) is dcons=inc = ^ 0=inc+ ^ 1. Using observations for 100 families on annual income

and consumption (both measured in dollars), it is obtained that

X100

i=1

inci = $31105;

X100

i=1

consi = $25105;

X100

i=1

inciconsi = 1:1251011;

X100

i=1

(inciinc)2 = 4:3211010;

where inc is the average income over the sample and summations are taken over the n = 100 families; R2 = :6

is obtained.

1. What are the average income and average consumption from this sample?

2. Give the numerical value of the OLS estimators ^ 0 and ^ 1 of 0 and 1, respectively.

3. Interpret ^ 0 in this regression model and comment on its sign and magnitude.

4. What is the predicted consumption when family income is $27,000?

5. Letting u be the regression error and assuming that 2 = V ar(uijX) = 2000, nd the numerical values of

V ar( ^ 1jX) and V ar( ^ 0jX), where X is the vector of income data collected on the sample.

6. Interpret the R2 of this regression.