# Fuel Consumptions Case (Multiple Linear Regression): Calculate confidence intervals

See the attached case study for proper format and tables.

(NOTE: Hypothesis testing only for independent variable slopes (b1 and b2). Calculate the 95% Confidence intervals for b1 and b2.)

3 THE FUEL CONSUMPTION CASE

Use the output in (Fig 1a) to do (1) through (6) for each of ?0, ?1, and ?2 .

(Fig-1a) t Statistics and p-Values for Four Case Studies

1 Find bj, sbj, and the t statistic for testing H0 : ?j = 0 on the output and report their values. Show how t has been calculated by using bj and sbj .

2 Using the t statistic and appropriate critical values, test H0 : ?1 = 0 versus Ha : ? 0 by setting a equal to .05. Which independent variables are significantly related to y in the model with a = .05?

3 Using the t statistic and appropriate critical values, test H0 : ?j = 0 versus Ha : ?j ? 0 by setting ? equal to .01. Which independent variables are significantly related to y in the model with ? = .01?

4 Find the p-value for testing H0 : ?j = 0 versus Ha : ?j ? 0 on the output. Using the p-value, determine whether we can reject H0 by setting a equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model?

5 Calculate the 95 percent confidence interval for ?j. Discuss one practical application of this interval.

6 Calculate the 99 percent confidence interval for ?j .

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(NOTE: Hypothesis testing only for independent variable slopes (b1 and b2). Calculate the 95% Confidence intervals for b1 and b2.)

3 THE FUEL CONSUMPTION CASE

Use the output in (Fig 1a) to do (1) through (6) for each of ?0, ?1, and ?2 .

(Fig-1a) t Statistics and p-Values for Four Case Studies

1 Find bj, sbj, and the t statistic for testing H0 : ?j = 0 on the output and report their values. Show how t has been calculated by using bj and sbj .

Solution:

b1 = -0.09011, Sb1 = 0.01408, t = -6.39, t = b1/Sb1 = -0.09011/0.01408 = -6.39

b2 = 0.08249, Sb1 = 0.02200, t = 3.75, t = b1/Sb1 = 0.08249/0.02200 = 3.75

2 Using the t statistic and appropriate critical values, test H0 : ?1 = 0 versus Ha : ? 0 by setting a equal to .05. Which independent variables are significantly related to y in the model with a = .05?

Solution:

Here Temp and Chill are the significant independent variables in the model with a = .05 as their p-values are less than 0.05.

Reject H(0) if |t|>t(alpha/2); t(alpha/2) = t(0.025) = 2.447 (at ...

#### Solution Summary

The solution finds the multiple linear regression for the Fuel Comsumptions Case.