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.

Solutions

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
Next > < Previous

Related Solutions

(a) Over the past decade, some of Japanese savings has been used to purchase large amounts...
(a) Over the past decade, some of Japanese savings has been used to purchase large amounts of U.S. financial assets (typically U.S. government bonds). Suppose Japan suddenly stopped purchasing U.S. financial assets. Graphically illustrate the effect of Japan’s reduction in purchases of U.S. financial assets using the Open Economy model developed in the Ch 6 appendix. (Hint: In your model you will need to draw three diagrams). Clearly label the axes and curves in each of your graphs in the...
The rate of entrepreneurship has been growing steadily in the United States over the past decade....
The rate of entrepreneurship has been growing steadily in the United States over the past decade. The reasons behind this increase are varied. Most of the people starting a business seek a combination of greater financial success, independence, flexibility, and challenge. Owning a business holds appealing benefits for entrepreneurs like being their own boss, having control over their schedule, and facing new challenges. Almost every entrepreneur starts out as a small businessperson but not every small businessperson starts out as...
The past decade has been marred by a series of scandals in South Africa’s private sector,...
The past decade has been marred by a series of scandals in South Africa’s private sector, each demonstrating a clear lack of ethics, each fraudulent in their own special way (Business Insider South Africa, 2020). With the aid of appropriate business related examples, critically debate the three (3) Ethical Models of Jones and George (2003) and advise the business community on the most suitable model for organisations to adopt.
Healthcare Policy in the United States has been largely consumed over almost the past decade by...
Healthcare Policy in the United States has been largely consumed over almost the past decade by Affordable Care Act. Why does universal access to healthcare continue to be debated in the United States, and in what ways is this discussion different from the healthcare discussion in other countries?
1 Over the past decade, there has been a strong positive correlation between teacher salaries and...
1 Over the past decade, there has been a strong positive correlation between teacher salaries and prescription drug cost. (a) Do you think paying teachers more causes prescription drugs to cost more? Explain. (b) What lurking variable might be causing the increase in one or both of the variables? Explain. 2 When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products continues to rise, so management has decided to expand the production facility; $2 800 000 has been set aside for this over the next four years. Management has developed two different plans for expanding over the next four years: Plan A and Plan B. Plan A would require equal amounts of $750 000, one year from now, two years from now, three years from...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products continues to rise, so management has decided to expand the production facility; $2 800 000 has been set aside for this over the next four years. Management has developed two different plans for expanding over the next four years: Plan A and Plan B. Plan A would require equal amounts of $750 000, one year from now, two years from now, three years from...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products continues to rise, so management has decided to expand the production facility; $2 800 000 has been set aside for this over the next four years. Management has developed two different plans for expanding over the next four years: Plan A and Plan B. Plan A would require equal amounts of $750 000, one year from now, two years from now, three years from...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products continues to rise, so management has decided to expand the production facility; $2 800 000 has been set aside for this over the next four years.Management has developed two different plans for expanding over the next four years: Plan A and Plan B. Plan A would require equal amounts of $750 000, one year from now,two years from now, three years from now, and...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products...
Precision Machining Corporation has been growing steadily over the past decade. Demand for the company’s products continues to rise, so management has decided to expand the production facility; $2 800 000 has been set aside for this over the next four years. Management has developed two different plans for expanding over the next four years: Plan A and Plan B. Plan A would require equal amounts of $750 000, one year from now, two years from now, three years from...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT