How many degrees of freedom and why Problem 4 Demand for aut

Problem 4: Demand for automobiles Based on data for the years 1962 to 1977 for the US, Dale Bails and Larry eppers obtained the following demand function for automobiles Y, = + axt = 5807 + 3.24%, n° = 0.22, se() = 1.634, where Y = retail sales of passenger cars (in thousands) and X = the real disposable income (in billions of 1972 dollars) ( a) Derive a 95% confidence interval for (b) Does this interval include = 0? Would you reject this null hypothesis? (c) Compute the t statistic under the Ho : = 0 . Is it statistically significant . at the 5% level?

Solution

In this case we have n-1 degrees of freedom

We have n samples and k unknown parameters that why we have n-k degree of freedom .

Hence degree of freedom will be n-1

95% interval will be (beta_hat+1.96*se(beta_hat),beta_hat-1.96*se(beta_hat))=(beta_hat+1.96*1.63;beta_hat-1.96*1.63)

To check beta=0 is whether significant or not

Then test score =(beta_hat)/se(beta_hat)=3.24/1.63=2

We will reject the hypothesis as test score is greater than 1.96