PUAF 610

Quantitative Methods in Policy Analysis

Fall 2007

Problem Set #8

1.

Below is the mass and cost of six U.S. solid-fuel ballistic missiles:

Missile

Mass

(tons)

Unit Cost

(million $FY87)

Lance

1.3

0.2

Pershing II

7.4

2.5

Poseidon C3

29.

5.0

Minuteman III

35.

7.8

Trident C4

30.

8.1

Peacekeeper

88.

22.0
 

A.

State an appropriate theory about the relationship between these two variables. Which should be the independent variable? Which should be plotted on the y-axis?

B.

Enter the data into a spreadsheet and construct a scatterplot. Using the "trendline" option, display the regression line and the equation on the scatterplot. Is the regression line a good fit?

C.

Explain the meaning of the slope and intercept in plain English. Do the values make sense?

D.

Now use Data Analysis to perform the regression analysis, and verify that the slope and intercept are equal to values computed above.

E. Formulate and test an appropriate null hypothesis, and state your conclusions in plain English.
F. Give the 95% confidence interval for the “true” slope, and interpret the result in plain English.

G.

Give the value of R2 and interpret it in plain English.

H.

The Navy has proposed to build a new solid-fuel missile with a mass of 57 metric tons.

   

i.

Based on your analysis above, what is your best guess for the cost of this new missile (in fiscal year 1987 dollars)?

  
   

ii.

How uncertain this estimate? In other words, what is the standard error? (You may give an approximate answer or, for 5 extra points, the precise value.)

 
   

iii.

Give a 99% confidence interval for the cost of the new missile. (HINT: take into account the correct degrees of freedom.)

  
   

iv.

The Navy builds the missile, which is known as the Trident II. The cost turns out to be $28 million dollars (in FY 1987 dollars). What do you conclude?

  
2.

Using the UMCPsalaries.xls data set and one of the regression tools, do a simple regression analysis using years since highest degree (yrdeg) and salary.

A.

Explain the meaning of the slope and intercept in plain English. Do these values make sense?
B. Explain the meaning of the R-squared value in plain English.
C. What is the null hypothesis? Do you reject or fail to reject the null hypothesis? How confident are you?

D.

Plot the residuals. What do you notice? Why does this pattern arise?