R has a number of datasets built in. One such dataset is called mtcars. This data set contains fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models) as reported in a 1974 issue of Motor Trend Magazine.

We do not have to read in these built-in datasets. We can just attach the variables by using the code

        attach(mtcars)

We can just type in mtcars and see the entire dataset. We can see the variable names by using the command

The variables are defined as follows:

mpg Miles/(US) gallon

cyl Number of cylinders

disp Displacement (cu.in.)

hp Gross horsepower

drat Rear

axle ratio

wt Weight (lb/1000)

qsec 1/4 mile time

vs V/S (“V” engine or “Straight line”) (0 or V, 1 for S)

am Transmission (0 = automatic, 1 = manual)
gear Number of forward gears
carb Number of carburetors

We want to model mpg by some or all of the other 10 variables . Do a complete regression analysis. Be sure to comment for each thing you do.

Suppose a prototype for a car was in development. This car has 6 cylinders, 250 cubic in. engine, 130 horsepower, a rear axle ratio of 3.8, weighs 2750 pounds, has a 1/4 mile time of 15.9 seconds, is a V engine type, has automatic transmission, 5 forward gears, and 6 carburetors. With 90% confidence, what is an interval estimate for the predicted mpg for this car?

1. Which of the following are factors that can shift the supply curve for concert tickets?

1. a wage increase for musicians
2. a cut in personal income taxes
3. a new sound system for concert halls
4. a subsidy for concert providers
5. the price of substitutes for concerts

a. I, II, and V only

b. I, III, and IV only

c. I, III, and V only

d. II, IV, and V only

e. I, III, IV, and V only

2. Given a normal market supply curve for automobiles, if the government required that side airbags be installed on all automobiles, then

a. there is an increase in supply of automobiles.

b. there is an increase in the quantity supplied of automobiles.

c. there is a decrease in supply of automobiles.

d. there is a decrease in the quantity supplied of automobiles.

e. cannot be determined from information given.

3. If the government institutes an effective price floor on volleyballs, then there will be a

a. decrease in demand for and an increase in supply of volleyballs.

b. decrease in supply of volleyballs.

c. decrease in quantity supplied of volleyballs.

d. decrease in demand for volleyballs.

e. decrease in quantity demanded for volleyballs.

4.

If the government sets a price ceiling of $4,

a. market forces will cause the quantity demanded to drop and the quantity supplied to rise.

b. a shortage will exist.

c. a surplus will exist.

d. market forces will cause demand to drop and supply to rise.

e. market forces will cause supply to drop and demand to rise.

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1.the High-Low Method, and

2. the Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program.

Make sure to report:

1. the values of v and f;

2. a scatter plot of the data points, and

3. the adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

***YOUR SUBMISSION MUST BE IN EXCEL. ***

***PLEAE INCLUDE AN EXCEL ATTACHMENT SO THAT I MAY OPEN IT UP IN EXCEL.***

***ONE WORKBOOK, WITH A WORKSHEET FOR EACH ANALYSIS***

(i.e., High-Low Method and Regression Analysis respectively). The regression analysis must include the output from the Analysis Datapak similar to Exhibit 6-15 on page 328.

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1. the High-Low Method, and

2. the Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program. Please follow the instructions on P.329 of the textbook; DIRECTIONS FOR ADD-Ins: Data Analysis Toolpak.

Make sure to report

1. the values of v and f;

2. a scatter plot of the data points, and

3. the adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

YOUR SUBMISSION MUST BE IN EXCEL. PLEASE INCLUDE AN EXCEL ATTACHMENT OR HYPERLINK! ONE WORKBOOK, WITH A WORKSHEET FOR EACH ANALYSIS (i.e., High-Low Method and Regression Analysis respectively).  

4.2.2 What is an RC Circuit?

Recall that the capacitance is defined as the proportionality constant between the total charge accumulated by a capacitor and the voltage difference across the circuit

Q = C△V (4.2)

In this equation, the charge Q is expressed in Coulomb (C), the voltage △V, in volts (V) and the capacitance C in farads (F).

In this lab you will study both the charging and discharging process of an RC circuit. During the charging process, an electrical EMF source accumulates charges on each side of the parallel plate capacitor. During the discharging process, the capacitor releases all its charges into the circuit (which now does not contain the battery). Capacitors charge and discharge exponentially in time. During the discharge of a capacitor, the instantaneous voltage △Vc between the ends of the capacitor also drops and is given by △Vс = △Vmax*e^(-t/τ) (4.3) where △Vmax is the maximum voltage across the capacitor, i.e. the voltage to which thecapacitor was initially charged, t is the time and τ is the time constant given by τ= Req*Ceq (4.4) where Req and Ceq are, respectively, the equivalent resistance and capacitance to which we can reduce the circuit. Although the theoretical discharge time is in nite, in practice we consider that the discharge is over when the voltage at the bounds of the capacitor is at 1% of its maximal value.

Answer the following questions in the Results section: Assuming the voltage, when completely charged, is set to V₀ = 1 and by considering the variables τ for time constant and t for time, what are the equations for of charging and discharging? Support your answer by physical arguments

Programming Language C++

Task 1: Write a program to calculate the volume of various containers. A base class, Cylinder, will be created, with its derived classes, also called child classes or sub-classes.

First, create a parent class, Cylinder. Create a constant for pi since you will need this for any non-square containers. Use protected for the members. Finally, create a public function that sets the volume.

// The formula is: V = pi * (r^2) * h

Task 2: Create a derived, or child class for Cylinder, that is, a Cone class. The same function, with the same parameters, is used. However, the formula is different for a cone.

// The formula is: V = (1/3) * pi * (r^2) * h

Task 3: Test your classes in the main function by creating an instance of Cone and an instance of Cylinder. In each case, call the set_volume function, passing the same parameters.

Task 4: Create a derived class for Cone called PartialCone. Add a second radius variable with scope specific to this class (because the top and bottom radii of a partial cone are different). Redefine the set_volume function.

The formula for the volume of a partial/truncated cone is:

• V = h * (PI / 3) * (R² + (R * r) + r² )
• V = volume
• R = base radius
• r = top surface radius

Task 5:

1. What happens if you change the access modifiers for Cylinder's variables to private?
2. Consider that you declare a private variable in the Cone class. Can you reference it in Cylinder?

A study compared three display panels used by air traffic controllers. Each display panel was tested for four different simulated emergency conditions. Twenty-four highly trained air traffic controllers were used in the study. Two controllers were randomly assigned to each display panel-emergency condition combination. The time (in seconds) required to stabilize the emergency condition was recorded. The following table gives the resulting data and the MINITAB output of a two-way ANOVA of the data.

Figure 12.12  

(a) Interpret the interaction plot in the above table. Then test for interaction with α = .05.

(b) Test the significance of display panel effects with α = .05.

F = 43.73, p-value = .0000;   (Click to select)   do not reject   reject  H₀

(c) Test the significance of emergency condition effects with α = .05.

F = 148.31, p-value = .0000;   (Click to select)   do not reject   reject  H₀

(d) Make pairwise comparisons of display panels A, B , and C by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(e) Make pairwise comparisons of emergency conditions 1, 2, 3, and 4 by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(f) Which display panel minimizes the time required to stabilize an emergency condition? Does your answer depend on the emergency condition? Why?

(g) Calculate a 95 percent (individual) confidence interval for the mean time required to stabilize emergency condition 4 using display panel B. (Round your answers to 2 decimal places.)

  Confidence interval         [  ,  ]

A study compared three display panels used by air traffic controllers. Each display panel was tested for four different simulated emergency conditions. Twenty-four highly trained air traffic controllers were used in the study. Two controllers were randomly assigned to each display panel-emergency condition combination. The time (in seconds) required to stabilize the emergency condition was recorded. The following table gives the resulting data and the MINITAB output of a two-way ANOVA of the data.

Figure 12.12  

(a) Interpret the interaction plot in the above table. Then test for interaction with α = .05.

(b) Test the significance of display panel effects with α = .05.

F = 29.73, p-value = .0000;   (Click to select)   do not reject   reject  H₀

(c) Test the significance of emergency condition effects with α = .05.

F = 75.70, p-value = .0000;   (Click to select)   do not reject   reject  H₀

(d) Make pairwise comparisons of display panels A, B , and C by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(e) Make pairwise comparisons of emergency conditions 1, 2, 3, and 4 by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(f) Which display panel minimizes the time required to stabilize an emergency condition? Does your answer depend on the emergency condition? Why?

(g) Calculate a 95 percent (individual) confidence interval for the mean time required to stabilize emergency condition 4 using display panel B. (Round your answers to 2 decimal places.)

  Confidence interval         [  ,  ]