# Regression Coefficients and Hypothesis Testing-53284

Properties of the Regression Coefficients and Hypothesis Testing

1)      Question is given as below:

Solution is given as below:

We are given,

b2* = ƛ2b2 where b2* is the slope coefficient………….(1)

Standard error of b2* = SE(b2*)

SE(b2*) = stdev(b2*) / sqrt(n)

SE(b2) = stdev(b2) / sqrt(n)………………….(2)

SE(b2*) = stdev(b2*) / sqrt(n)

SE(b2*) = stdev(ƛ2b2) / sqrt(n)

SE(b2*) = ƛ2 stdev(b2) / sqrt(n)…………….taking constant ƛ2 outside

SE(b2*) = ƛ2 SE(b2)………………(By using 2)

Question: 2

A researcher hypothesis that years of schooling, S, may be related to the number of siblings (brothers and sisters), SIBLINGS, according to the relationship given below:

She is prepared to test the null hypothesis H0: B2 = 0 against the alternative hypothesis Ha: B2 ≠ 0 at the 5 percent and 1 percent levels. She has a sample of 60 observations. What should she report?

Solution:

According to the null hypothesis, she should be get the value for b2 as closer as B2.

The closer value is given as b2 = 0.06, so the correct alternative for this question is the option c which is given as below:

c) if the b2 = 0.06, standard error or S.E. (b2) = 0.07