Practical 9 Task 4 (with answer explanations)

Identify the variables used in this analysis.

• Explanatory variable: Age

  Response variable: Number of breakdowns

• Explanatory variable: Number of breakdowns

  Response variable: Age

Using Minitab, what is the equation of the least-squares regression line?

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Answer explanation

Conduct a test with the hypotheses H₀: β = 0 vs H₁: β ≠ 0 to see if there is a statistically significant relationship between age and number of breakdowns. Assume α = 0.05.

What is the P-value?

Answer explanation

Conduct a test with the hypotheses H₀: β = 0 vs H₁: β ≠ 0 to see if there is a statistically significant relationship between age and number of breakdowns. Assume α = 0.05.

Interpret the P-value obtained.

• As P-value ≈ 0 < α = 0.05, H₀ is rejected. β is significantly different from 0. There is a significant linear relationship between age and number of breakdowns.

• As P-value = 0.106 > α = 0.05, H₀ is not rejected. β is not significantly different from 0. There is no significant linear relationship between age and number of breakdowns.

• As P-value = 0.028 < α = 0.05, H₀ is rejected. β is significantly different from 0. There is a significant linear relationship between age and number of breakdowns.

• As P-value ≈ 0 < α = 0.05, H₀ is rejected. ρ is significantly different from 0. There is a significant linear relationship between age and number of breakdowns.

What is the slope of the regression line? Give your answer correct to 3 d.p.

Answer explanation

Interpret the slope of the regression line.

• For every 1 year increase in age, predicted number of breakdowns increases by 0.989 on average.

• For every 1 year increase in age, predicted number of breakdowns decreases by 0.989 on average.

• For every 0.989 year increase in age, predicted number of breakdowns increases by 1 on average.

• For every 0.989 year increase in age, predicted number of breakdowns decreases by 1 on average.

Predict the number of breakdowns for a machine of age 5 years. Give your answer correct to 2 d.p.

Answer explanation

Predict the average number of breakdowns for a machine of age 15 years.

• 12.92

• 16.53

• 17.11

• Not applicable, as a machine of 15 years is out of range of the data used to fit the model (extrapolation)

Answer explanation

What is the value of R²? (Correct to 1 d.p.)

Answer explanation

Interpret the R² obtained.

• 93.9% of the variation in the number of breakdowns can be explained by the fitted model.

• 93.9% of the variation in the age can be explained by the number of breakdowns.

• 93.9% of the number of breakdowns is due to age.

• There is a strong positive linear relationship between age and number of breakdowns.