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"Employment Regression in Private Shipyards: Naval Vessels & Commercial Repairs" - Prof. K, Study notes of Humanities

Data on private shipyard employment figures, number of naval vessels under construction, and number of repairs or conversions of commercial ships over a 7-year period. The document aims to develop a regression model to predict private shipyard employment using the given variables.

Typology: Study notes

2011/2012

Uploaded on 02/27/2012

kaitlin-wilhelm
kaitlin-wilhelm 🇺🇸

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1) The ship builders Council of America in Washington, D.C., publishes data about private
shipyards. Among the variables reported by this organization are the employment figures
(per 1000), the number of naval vessels under construction, and the number of repairs or
conversions done to commercial ships (in $ millions). Shown here are the data for the three
variables over a 7-year period. Use the data to develop a regression model to predict private
shipyard employment from number of naval vessels under construction and repairs or
conversions of commercial ships.
If simple linear regression were used, the scatterplot for each independent variable is above.
a) Do either or both of the above plots suggest a relationship?
Minitab output
Predictor Coef SE Coef T P
Constant 35.91 53.34 0.67 0.531
naval vessles 0.8291 0.5880 1.41 0.218
repairs of conversions 0.02189 0.01946 1.12 0.032
S = 18.8224 R-Sq = 64.8% R-Sq(adj) = 50.72%
Analysis of Variance
Source DF SS MS F P
Regression 2 2144.2 (E) 3.03 0.138
Residual Error 5 (D) 354.3
Total 7 3915.6
b) What is the equation of the line and define the pieces.
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1) The ship builders Council of America in Washington, D.C., publishes data about private

shipyards. Among the variables reported by this organization are the employment figures

(per 1000), the number of naval vessels under construction, and the number of repairs or

conversions done to commercial ships (in $ millions). Shown here are the data for the three

variables over a 7-year period. Use the data to develop a regression model to predict private

shipyard employment from number of naval vessels under construction and repairs or

conversions of commercial ships.

If simple linear regression were used, the scatterplot for each independent variable is above.

a) Do either or both of the above plots suggest a relationship?

Minitab output

Predictor Coef SE Coef T P

Constant 35.91 53.34 0.67 0.

naval vessles 0.8291 0.5880 1.41 0.

repairs of conversions 0.02189 0.01946 1.12 0.

S = 18.8224 R-Sq = 64.8% R-Sq(adj) = 50.72%

Analysis of Variance

Source DF SS MS F P

Regression 2 2144.2 (E) 3.03 0.

Residual Error 5 (D) 354.

Total 7 3915.

b) What is the equation of the line and define the pieces.

c) Discuss the R^2 - adjusted.

d) How big is the initial sample?

For 2-3, circle the best answer.

2) In simple regression analysis, if the coefficient of determination is a positive value, then

A) The Y intercept must also be a positive value.

B) The correlation coefficient can be either positive or negative, depending on the value

of the slope.

C) The slope of the regression line must also be negative.

D) The slope of the regression line must be positive.

E) The standard error of estimate can either have a positive or a negative value.

3) If the coefficient of correlation for a model is .601, what is the coefficient of determination?

a) .849 b) .720 c) .518 d) -.849 e).

4) Executives of a video rental chain want to predict the success of a potential new store. The

company’s researchers begin by gathering information on a number of rentals and average

family income (in thousands of dollars) from several of the chain’s present outlets.

Table

rentals average family income 710 65 529 43 314 29 504 47 619 52 428 50 317 46 205 29 468 31

e) Test to see if the slope exists at α = .05. Set up the null and alternative hypothesis and make a

decision.

f) If a family makes $60,000 a year, how many video rentals do we expect that they will rent?