Question

In: Statistics and Probability

For the past decade, rubber powder has been used in asphalt cement to improve performance. An...

For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:

x	112.3	97.0	92.7	86.0	102.0	99.2	95.8	103.5	89.0	86.7
y	74.5	71.0	57.4	48.7	74.6	73.6	67.8	59.7	58.2	48.7

(a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)
y =

Interpret the slope.

A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope.

(b) Calculate the coefficient of determination. (Round your answer to four decimal places.)

Interpret the coefficient of determination.

The coefficient of determination is the number of the observed samples of axial strength of asphalt that cannot be explained by variation in cube strength. The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that cannot be attributed to its linear relationship with cube strength. The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that can be attributed to its linear relationship with cube strength. The coefficient of determination is the number of the observed samples of axial strength of asphalt that can be explained by variation in cube strength.

(c) Calculate an estimate of the error standard deviation σ in the simple linear regression model. (Round your answer to three decimal places.)
MPa

Interpret the estimate of the error standard deviation σ in the simple linear regression model.

The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than one error standard deviation. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within one error standard deviation. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within two error standard deviations. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than two error standard deviations.

Expert Solution

a)

y^ =0.9768+(-30.7585)*x

A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope

b)

SST=Syy=		938.7160
SSE =Syy-(Sxy)²/Sxx=		353.088
SSR =(Sxy)²/Sxx =		585.6277

Coeffficient of determination R^{^2} =SSR/SST=

0.6239

The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that can be attributed to its linear relationship with cube strength.
c)

a	s² =SSE/(n-2)=	44.1360
std error σ =	=se =√s²=	6.643

The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within one error standard deviation

orchestra answered 1 year ago

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For the past decade, rubber powder has been used in asphalt cement to improve performance. An...

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