Question

1) Use the following information from a multiple regression analysis to complete parts​ (a) through​ (c) below.

n =25    b₁ =30    b ₂ =10    S_b1=8    S_{b 2} =6

b) Construct a​ 95% confidence interval estimate of the population​ slope, β1.

____≤β1≤_____ ​(Round to four decimal places as​ needed.)

c) At the 0.05 level of​ significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these​ results, indicate the independent variables to include in this model.

--- Find the test statistic ____ --- Find the p-value _____

Is there evidence that the variable X1 contributes to a model already containing X2?

A.Yes​,since the null hypothesis is not rejected.

B.Yes​, since the null hypothesis is rejected.

C.No​,since the null hypothesis is not rejected.

D.No​,since the null hypothesis is rejected.

Choose the correct hypotheses for X₂?

Find the test statistic (round two decimal places) ----- Find the p-value(round 3 decimal places)

Is there evidence that the variable X2 contributes to a model already containing X1?

A.Yes​,since the null hypothesis is not rejected.

B.No​,since the null hypothesis is rejected.

C.Yes​,since the null hypothesis is rejected.

D. No​,since the null hypothesis is not rejected.

  On the basis of these​ results, indicate the independent variables to include in this model. Choose the correct answer below.

A. Include only the variable X1.

B. Include neither variable X1 nor X2.

C. Include both variables X1 and X2.

D. Include only the variable X2.

Answer 1

b)

n =   25
alpha,α =    0.05
estimated slope=   30
std error =    8
Df =    n - 2 =   23
critical t-value =    2.0687 [excel function =t.inv(0.05/2,23) ]

confidence interval is      
lower bound = estimated slope - E=   13.4507
upper bound = estimated slope + E=   46.5493
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c)

Ho:   ß1 = 0
Ha:   ß1 ╪ 0

t-test statistic =    t = estimated slope / std error =   3.75

p-value =    0.0010

p-value <α=0.05 , reject Ho

yes, there evidence that the variable X1 contributes to a model already containing X2

.Yes​, since the null hypothesis is rejected

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d)

Ho:   ß2 = 0
Ha:   ß2 ╪ 0

n =   25
alpha,α =    0.05
estimated slope=   10
std error =    6
  
t-test statistic =    t = estimated slope / std error =   1.67
      
Df =    n - 2 =   23
p-value =    0.1091  
since,p-value >α=0.05 , so do not reject Ho.

No, there is no evidence that the variable X2 contributes to a model already containing X1

No​,since the null hypothesis is not rejected

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A. Include only the variable X1. [ because only variable X1 is significant]