## Linear Regression

a) Obtain time series of real GDP and real consumption for a country of your choice. Provide details.(b) Display time-series plots and a scatterplot (put consumption on the vertical axis).(c) Convert your series to growth rates in percent, and again display time series plots.(d) For each series, ,provide summary statistics (e.g., mean, standard deviation, range, skewness, kurtosis,…).(e) Run a simple OLS linear regression in R and interpret its coefficient estimates.(f) Interpret goodness-of-fit metrics for OLS linear regression.(g) Relate R2 with correlation coefficient.Problem 2Monte Carlo experiment: Consider the following model:Yi = ?1 + ?2Xi + uiYou are told that ?1 = 25,?2 = 0.5,? 2 = 9, and ui ? N(0, 9).Assume ui ? N(0, 9), that is, ui are normally distributed with mean 0 and variance 9. Generate 10 sets of64 observations on ui from the given normal distribution and use the 64 observations on X given in Table 2, to generate 100 sets of the estimated ? coefficients (each set will have the two estimated parameters). Takethe averages of each of the estimated ? coefficients and relate them to the true values of these coefficientsgiven above. What overall conclusion do you draw?1

## A Linear Cipher

Encryption is present in all aspects of information technology. Any information that you want to keep secret should be encrypted, and only the intended recipient should have the key to decrypt.For as long as ciphers have existed to encrypt information, hackers have existed who attempt to crack the key and illicitly decipher the message.In this discussion, you will first encrypt information using a linear cipher. Then, you will become the hacker and discuss ways to crack one anothers messages.For this Discussion:Write a short message of between 15 and 40 characters to your classmates. Encode it using a linear affine cipher with n=26. Post the message to the Encrypted Messages thread but do not give the a and b that you utilized.Also post your own initial response thread in which you propose at least one way that you might try to decipher messages without the key.

## A Computer Algorithmically

Think first of a network of roads for GPS mapping. Every road whether in a neighborhood or spanning states is included in possible paths. A dirt road is included in the overall network just like a major highway. Clearly, it is impossible to consider every possible path in every GPS mapping decision. If traveling from your house to the nearest grocery store, it is absurd to consider paths that go through another city 800 miles away. If driving from the Empire State building in New York City to the Golden Gate Bridge in San Francisco, a dirt road in Iowa might be close to on the way but doesnt need to be considered as a path.The Internet is similar to that mesh of roads with connections ranging from local cable lines to submarine optical cables traversing thousands of kilometers. Just like with the roads, not all possible paths in the network need to be considered for every packet route.Consider methods to narrow down these paths for GPS mapping or mesh network routing. What strategies and processes might be applied to have a computer algorithmically do what a person glancing at a map does naturally?For this Discussion:Choose either the GPS map routing or the Internet routing. Describe an algorithm for quickly determining the best path to take within such a broad mesh. Provide an example to show how the algorithmic process would determine a specific route for an automobile or data packet.

## Graphing Island

Your population is thriving on your island. The data you have collected now needs to be displayed and further analyzed. Use the charts you created in the probability portion in weeks 1-3 for this part of the project. Always show your calculations or explain how you used technology. Take a picture of your calculator if you used that or submit your excel worksheet.1. a. Create a Scatter Plot using the total population for each of the years from the Probability Island. The horizontal axis should always represent time.b. Use linear regression or a trendline in Excel to find the equation of the best fit line.c. Find the Correlation Coefficient. Explain what this means for your data.d. Use the equation to predict the population in year 20.2. a. Use the first and last data points of the total population for each of the years from the Probability Island to find a linear equation to model the data.b. Graph the equation.c. Compare the slope of the Linear Regression Line of question 1 with the slope of this line. Provide an explanation of why they may similar or differ.d. Use the equation to predict the population in year 20.3. a. Assume that (0,150) represents the vertex of a quadratic equation. Find a quadratic equation using the tenth-year population as another point.b. Graph the equation.c. Use the equation to predict the population in year 20.4. Using the equation y = 2×2 -9x +4, explain and demonstrate how to find the x-intercepts, the y-intercept, the axis of symmetry, and the vertex of a quadratic equation.

## Cumulative Distribution Functions

Comparison of Cumulative Distribution Functions for cost associated with Contract A andContract Ba) What are the realistic maximum and minimum costs associated with each of the contracts?[4 marks]b) Which contract is associated with a higher probability of a cost less than £8 million? Whichcontract is associated with a higher probability of a cost greater than £11 million?[2 marks]c) If your decision was based on minimizing the expected value of the cost, which contractwould you choose? Does this agree with your assessment in Q5c, and if not, why not?

## Effectiveness of Criminal Justice

Respond to the following in a minimum of 175 words:In your opinion, how have statistics been used effectively by criminal justice professionals? Provide recommendations for more effective use and incorporation by criminal justice professionals.What are some examples of the effectiveness of criminal justice research in finding solutions to problems?

## Coterminal Angles

Explain how to find coterminal angles. How does this process differ for angles given in radians verses angles given in degrees? For #15-18, find an angle between ?? and ???? coterminal to the given angle. Give your answer in radians. 16. &%!