Mathematics, 10.03.2020 06:53 rdemp6105

Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of significance? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Answers: 1

Show answers

Answers

Answer from: melanie1759

Step-by-step explanation:

Hello!

Given the data of the multiple linear regression (see attachment) You have to conduct the individual tests for the five independent variables proposed to determine which one is significantly relevant for the regression.

The individual hypothesis tests of the multiple regression are the same as conducting the analysis for simple linear regression. The parameter of interest will be the population slope of the given variable, βi, and the statistic will be the Student's t: $t= \frac{b_i-\beta_i }{Sb} ~ t_{n-2}$

All hypothesis tests will be two tailed, so using α: 0.05, the critical region and decision rule for the five tests will be:

$t_{n-2;\alpha /2}= t_{23;0.025}= -2.069$

$t_{n-2;1-\alpha /2}= t_{23;0.975}= 2.069$

If $t_{H_0}$ ≤ -2.069 or if $t_{H_0}$ ≥ 2.069, then the decision is to reject the null hypothesis.

If -2.060< $t_{H_0}$ <2.069, then the decision is to not reject the null hypothesis.

Individual tests:

For X₁

H₀: β₁=0

H₁: β₁≠0

α:0.05

b₁= 4.00

Sb₁= 1.50

$t_{H_0}$ = 2.00

Since -2.060< $t_{H_0}$ <2.069, the decision is to not reject the null hypothesis.

For X₂

H₀: β₂=0

H₁: β₂≠0

α:0.05

b₂= 3.00

Sb₂= 0.20

$t_{H_0}$ = 15.00

Since $t_{H_0}$ ≥ 2.069, the decision is to reject the null hypothesis.

For X₃

H₀: β₃=0

H₁: β₃≠0

α:0.05

b₃= 0.20

Sb₃= 0.05

$t_{H_0}$ = 4.00

Since $t_{H_0}$ ≥ 2.069, the decision is to reject the null hypothesis.

For X₄

H₀: β₄=0

H₁: β₄≠0

α:0.05

b₄= –2.50

Sb₄= 1.00

$t_{H_0}$ = –2.50

Since $t_{H_0}$ ≤ -2.069, the decision is to reject the null hypothesis.

For X₅

H₀: β₅=0

H₁: β₅≠0

α:0.05

b₅= 3.00

Sb₅= 4.00

$t_{H_0}$ = 0.75

Since -2.060< $t_{H_0}$ <2.069, the decision is to not reject the null hypothesis.

Even though it seems that the five independent variables altogether conform to a good regression model to explain/ predict the dependent variable. Individually there is not significant evidence to conclude that X₁ and X₅ are good predictors of Y. Therefore the model could work just as well using only X₂, X₃, X₄ as explanatory variables or there is a chance that without those two variables the regression will be even stronger.

I hope it helps!

Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of

Answer from: Quest

Iknow one of the answers is a and maybe b but not 100% sure about b
And do not get it wrong . this is a quiz and im struggling ! ☹️

Answer from: Quest

inverse property is the answer

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:50

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

Answers: 2

Answer

Mathematics, 21.06.2019 20:10

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Find the zeros of each function. f(x) = x^2 + 5x - 6

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.