Question

It has been speculated that there is a linear relationship between Oxygen and Hydrocarbon Levels. Specifically, Oxygen purity is assumed to be dependent on Hydrocarbon levels. A linear regression is performed on the data in Minitab, and you get the following results:

Regression Analysis: Purity-y versus Hydrocarbon level-X

Predictor              Coef SE Coef      T      P

Constant             74.283    1.593 46.62 0.000

Hydrocarbon level-X 14.947    1.317 11.35 0.000

S = 1.08653   R-Sq = 87.7%   R-Sq(adj) = 87.1%

Analysis of Variance

Source          DF      SS      MS       F      P

Regression       1 152.13 152.13 128.86 0.000

Residual Error 18   21.25    1.18

Total           19 173.38

1. What is the equation of the linear regression model?

a) y = 74.283 + 1.593x    b) y = 14.947 + 1.317x         

c) y = 74.283 + 14.947x   d) y = 1.593 + 1.317x

2. Using the regression equation: if you have a hydrocarbon level of 0.09, what is the predicted oxygen purity?

a) 75.65                        b) 16.08               c)   87.14                d) 2.72

Based on the results of the above regression and the ANOVA analysis, verify if the following statements are correct

3. The P-values for the correlation analysis are very small, suggesting that the coefficients of the linear model play an insignificant role in the relationship between hydrocarbon and oxygen purity

a) true                           b) false

4. The results from the ANOVA analysis do not support those from the regression analysis

a) true                           b) false

5. The P-value of the ANOVA analysis suggests that the null hypothesis should be rejected

a) true                           b) false

6. The ANOVA test suggests that the slope of the linear regression model is not null

a) true                           b) false

Answer 1

1. What is the equation of the linear regression model?   

c) y = 74.283 + 14.947x  

1. Using the regression equation: if you have a hydrocarbon level of 0.09, what is the predicted oxygen purity?

a) 75.65   

Based on the results of the above regression and the ANOVA analysis, verify if the following statements are correct

1. The P-values for the correlation analysis are very small, suggesting that the coefficients of the linear model play an insignificant role in the relationship between hydrocarbon and oxygen purity

b) false

1. The results from the ANOVA analysis do not support those from the regression analysis

b) false

1. The P-value of the ANOVA analysis suggests that the null hypothesis should be rejected

a) true

1. The ANOVA test suggests that the slope of the linear regression model is not null

a) true