Question

Use the following linear regression equation to answer the questions.

x₃ = ?16.6 + 3.7x₁ + 8.6x₄ ? 1.9x₇

If x₄ decreased by 2 units, what would we expect for the corresponding change in x₃?


(e) Suppose that n = 20 data points were used to construct the given regression equation and that the standard error for the coefficient of x₄ is 0.924. Construct a 90% confidence interval for the coefficient of x₄. (Round your answers to two decimal places.)

lower limit
upper limit

(f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x₄ is different from zero. (Round your answers to two decimal places.)

t	=
t critical	= ±

Conclusion

Reject the null hypothesis, there is sufficient evidence that ?₄ differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ?₄ differs from 0.     

Reject the null hypothesis, there is insufficient evidence that ?₄ differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ?₄ differs from 0.

Explain how the conclusion has a bearing on the regression equation.

If we conclude that ?₄ is not different from 0 then we would remove x₁ from the model.

If we conclude that ?₄ is not different from 0 then we would remove x₇ from the model.    

If we conclude that ?₄ is not different from 0 then we would remove x₄ from the model.

If we conclude that ?₄ is not different from 0 then we would remove x₃ from the model.

Answer 1

1) If x4 decreased by 2 units, what would we expect for the corresponding change in x3 =8.6*2=17.5

e)

for (n-4=16) degree of freedom and 90% confidence interval critical t=1.746

lower limit =estimate -t*std error =8.6-1.746*0.924=6.99 ( please try 6.98 if this comes wrong)

upper limit=estimate +t*std error =8.6+1.746*0.924=10.21 ( please try 10.22 if this comes wrong)

f)

t =8.6/0.924=9.31

tcriical =1.75

conclusion:Reject the null hypothesis, there is sufficient evidence that ?4 differs from 0.

If we conclude that ?4 is not different from 0 then we would remove x4 from the model.