The Strategic Air Command (SAC) is concerned about the possibility that missiles will not launch successfully.

 

3. MBB Problem 20.12 (modified): The Strategic Air Command (SAC) is concerned about the possibility that missiles will not launch successfully. Utilizing test data, it regresses X₁(the temperature at launch in degrees Fahrenheit), X₂(the number of months since the last overhaul of the launch mechanism), and X₃(the number of ICBMs sited within 800 meters). SAC gets the following results with Y (a dummy variable that is coded 1 if the launch fails):

 ; s.e._b1 = 0.0021; s.e._b2 = 0.0015; s.e._b3 = 0.087; R² = .69; n = 214.

(a)Interpret the slope for X₁.

(b)Interpret the slope for X₂.

 (c)Interpret the R-squared.

(d)Test the slope of X₁ for significance.

(e)Test the slope of X₂ for significance.

(f)SAC wants the probability of failure to be no more than 20%. If launches will proceed at -10 degrees with no other missiles within 800 meters, how often should launch mechanisms be serviced?

4. MBB Problem 20.14 (modified):The state tax division is evaluating the money raised by state sales taxes. Using data from all states, division members regress the amount of money raised by the sales tax per capita on the average per-capita income (X₁) and a dummy variable coded 1 if the state taxed the sale of groceries (X₂). They get the following results:

; s.e._b1 = 0.0043; s.e._b2 = 36.3; R² = .86; n = 50.

(a)Interpret the slope for X₁.

(b)Interpret the slope for X₂.

 (c)Interpret the R-squared.

(d)Test the slope of X₁ for significance.

(e)Test the slope of X₂ for significance.

(f) How much could a state with a per-capita income of $33,947 and a tax on groceries raise per capita with a sales tax?

 MBB Problem 20.20 (modified): Officials in the Michigan Department of Education want to determine why student performance varies across school districts in the state. Department officials ask their chief statistician to run a regression analysis where the average district pass rate on the state-mandated standardized skills test is the dependent variable (TEST). The independent variables are the average teacher salary per school district (TSAL), the average class size (CLSIZE), and the average district daily attendance rate (ATTEND). (Note: The data set for this problem is posted on Blackboard.)

 (a)Interpret the slope for TSAL.

(b)Interpret the slope for CLSIZE.

(c)Interpret the slope for ATTEND.

 (d)Interpret the R-squared.

(e)Interpret the p-value of the slope coefficient for TSAL.

(f)Interpret the p-value of the slope coefficient for CLSIZE.

(g)Interpret the p-value of the slope coefficient for ATTEND.

(h) The Bluewater School District has an average teacher salary of $40,000, an average class size of 15 students, and an average daily attendance rate of 95 percent. What should the statistician predict for Bluewater’s average pass rate?