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 H_a: 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