A consumption function is an economic relationship between consumption and incom

Question

A consumption function is an economic relationship between consumption and income in aggregate terms. This function is estimated by OLS and the results are showed below. Specifically, the dependent variable is the household consumption (C) and the only explicative variable is the household income (I), those observations are weekly recorded and expressed in real terms. The sample size and number of parameters to estimate are N = 15 and K = 2 respectively. The standard errors are provided and they are below the parameters or point estimates. (a) What is the type of data we are dealing with? What is the frequency of those data? (b) Is the coefficient related to income or slope (or marginal propensity to consume) significant in statistical terms?. (c) Construct a 99%, 95% and 90% confidence intervals for the constant and slope. Interpret those confidence intervals.

Explanation / Answer

(a) this is consumption and income relationship data , we want to fit regression line when consumption is dependent and income is independet variable

(b) we use t-test for testing of significance of slope and

t=coefficient/SE(coefficient)=0.493945/0.0461=10.71 with error df=14-1=13

with 99% confidence the two tailed critical t(0.01,13)=3.01 is less than calculated t=10.71, so at 1% level of significance slope is significant

here N=15. so total df=N-1=15-1=14

K=2, so regression model df=K-1=2-1 and

error df=total df - model df=(N-1)-(K-1)=14-1=13

(c) (1-alpha)*100% confidence interval for coefficient =coefficient±margin of error

=coefficient±t(alpha/2,error df)*SE(coefficeint)

confidence interval confidence % alpha=1-confidence t(error df) constant SE(constant) margin of error lower limit upper limit 99 0.01 3.012275833 28.264 8.1789 24.63710281 3.62689719 52.9011028 95 0.05 2.160368652 28.264 8.1789 17.66943917 10.5945608 45.9334392 90 0.1 1.770933383 28.264 8.1789 14.48428704 13.779713 42.748287 confidence interval confidence % alpha=1-confidence t(error df) slope SE(slope) margin of error lower limit upper limit 99 0.01 3.012275833 0.493945 0.0461 0.138865916 0.35507908 -0.3089791 95 0.05 2.160368652 0.493945 0.0461 0.099592995 0.39435201 -0.348252 90 0.1 1.770933383 0.493945 0.0461 0.081640029 0.41230497 -0.366205

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