Question

# Use the following linear regression equation to answer the questions. x3 = ?16.6 + 3.7x1 +...

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.

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.

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