Econometric: need help!?

Question

In a cross-section study of the consumer behavior of 10 families, the summary statistics for the relation between consumption (C), income (Y) and the number of children in the household (N) the summary statistics of the data are given as (data are scaled to $1000):

ΣC = 140 ΣY = 170 ΣN = 30 Σ c2 = 144 Σ y2 = 348 Σ n2 = 14

Σ yc = 215 Σ yn = 57 Σ nc = 39

Where c, y and n are the deviations of consumption, income and number of children form their corresponding means, respectively.

a- Do an OLS estimate of the consumption function.

b- Find the relevant statistics of the regression and the regression coefficients.

c- Find the relevant statistics of the regression and the regression coefficients.

d- Test the regression for the existence of multi-colinearity.

e- Write a 95% confidence interval for the estimated coefficient of Y and N.

f- Do a hypothesis test (at the .05 level) that the estimated MPC is less than 1.

Answer 1

a -

C=Β¹ + Β²Y

Β² = 215/348= 0.617816

Β¹ = ∑C /Q - Β² ∑Y/Q=14 - 0.617816 x 17 = 3.497126

C= 3.497126 + 0.617816 * Y

b+c -

For CN

Regression coeficent = 2.78571428571429

Intercept = 5.64285714285714

For CY

Regression coeficent = 0,617816091954

Intercept = 3,497126436782

For CN

Standard Error =2.10229466468021

Significance F =0.00110967188312135

For CY

Standard Error =1.18160591092616

Significance F =0.0000102209086660734

d -

Variable... Tollerance...VIF

Y................ 0,333...3,002

N................ 0,333...3,002

e -

95% Confidence Interval

Variable..Lower Bound ........Upper Bound

C............ 0.855758622............ 5.788726899

Y............. 0.248681383............ 0.721127613

N............ -0.366275867............ 1.989196385