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

*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

*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**

*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

*The results from the ANOVA analysis do not support those from the regression analysis*

a) true b) false

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

a) true b) false

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

a) true b) false

Answer #1

*What is the equation of the linear regression model?*

c) y = 74.283 + 14.947x

*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**

*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

*The results from the ANOVA analysis do not support those from the regression analysis*

b) false

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

a) true

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

a) true

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Source of Variation
SS
df
MS
F
P-value
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4
18051.89
7.770119
0.00003
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1
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SS
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1
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1300
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MS
F
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1
61,091.6455
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10
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