Curve-fitting Project - Linear Model

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r² (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.

A Linear Model Example and Technology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately.  (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative description in the title of your posting. Each student must use different data.)

The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.

(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)

(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.

(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.

(LR-5) Find and state the value of r², the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.

(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

A psychologist conducted an experiment analysing the relationship between student scores in an exam and the amount of attention they paid in class. The latter was measured using a type of brain monitor. The Psychologist believed that scores would increase by 1 for every two unit increase in attention. The data are listed in the excel spreadsheet.

Estimate a linear regression between the score (Y) and the measure of attention(X).

(a) Write out the equation for Y in the form , but with coefficients. Show the estimated standard errors in parenthesis below the coefficients. What is the R2 of the regression? Calculate a 99 percent confidence interval for β.                                                               [5 pts]

(b) What are the mean and the estimated standard deviation of the estimated residuals? [2 pts]

Hint: the first answer is definitional and the second answer is easily seen from the output.

(c )Test the hypothesis that there is no relationship between the variables at the 90 percent significance level.                                                                                                    [3 pts]

(d) Test the hypothesis that the coefficient β=0.5 at the 99% significance level.               [3 pts]

(e) The Psychologist concluded from the experiment that test scores increase significantly if students pay attention in class. In one word, how would you describe the results of this experiment based on the data you have?                                                                                                       [2 pts]

DATA:

Question 3

Amritha Singh is a middle manager with Coaster Plus Ltd (Coasters), a company that designs and manufactures roller coasters for amusement parks across North America. She has been appointed one of the project managers for the design and delivery of a special roller coaster for the Ultimate Park Ltd, an American customer. A major component of the project is the steel tracking, and one possible source is Trackers Canada Ltd (Trackers). Amritha’s supervisor has asked her to negotiate the necessary contract. Amritha began negotiations with Jason Hughes. Jason is a representative of Trackers, the steel tracking manufacturer willing to supply tracking to Coasters, Amritha’s employer. Amritha provided Jason with the plans and specifications for the roller coaster, and they negotiated a number of points, including price, delivery dates, and tracking quality. A short time later, Jason offered to sell Coasters a total of 900 metres of track in accordance with the plans and specifications provided. Jason’s offer contained, among other matter, the purchase price ($1.5 million), delivery date, terms of payment, insurance obligations concerning the track, and a series of warranties related to the quality and performance of the tracking to be supplied. There was also a clause, inserted at Amritha’s express request, which required Trackers to pay $5000 to Coasters for every day it was late in delivering the tracking.

After renewing the offer several days, Amritha for several days, Amritha contacted Jason and said, “You drive a hard bargain, and there are aspects of your offer that I’m not entirely happy with. However, I accept your offer on behalf of my company. I’m looking forward to doing business with you.”

Within a month, Trackers faced a 20% increase in manufacturing costs owing to an unexpected shortage in steel. Jason contacted Amritha to explain this development and worried aloud that without an agreement from Coasters to pay 20% more for the tracking, Trackers would be unable to make its delivery date. Amritha received instructions from her supervisor to agree to the increased purchase price in order to ensure timely delivery. Amritha communicated this news to Jason, who thanked her profusely for being so cooperative and understanding.

Jason kept his word and the tracking was delivered on time. However, Coasters has now determined that its profit margin on the American deal is lower than expected, and it is looking for ways to cut costs Amritha is told by her boss to let Jason know that Coasters will not be paying the 20% price increase and will remit payment only in the amount set out in the contract. Jason and Trackers are stunned by this development.

Applying the relevant principle(s) of contract law discuss the following questions:

a) Whether the negotiations between Jason and Amritha have legal consequences. (3 marks)

b) Discuss specific applicable ways by which each party mentioned above could have avoided the contract and as well as the implications of each way identified. (4 marks)

c) Discuss the consequences of the instruction of Amritha’s boss to the effect that Coasters will not be paying the 20% price increase and will remit payment only in the amount set out in the contract. (4 marks)

Objectives:

        The objectives of this lab exercise are to:

1. Demonstrate an understanding of the concept of operator precedence in Python expressions and statements.
2. Take simple problem descriptions and produce small but complete Python programs that solve these problems.
3. Give you some practice in using simple Python interactive input and output capabilities.
4. Give you some practice in the simplest Python decision statement (if).
5. Give you some practice in the simplest Python loop statement (while).

Specifications:

This is a four-part exercise.

1. For the three assignment statements listed below, label the operators according to the order they will be evaluated, i.e., label the first evaluated operator with a 1, the second with a 2, and so on.   Then fill in the blank with the result assigned to variable x in each part.

                        i.    x = 7 + 3 * 6 / 2 – 1                                                                                                                       

                                 x = ________

                        ii.   x = 2 % 2 + 2 * 2 – 2 / 2                                                                                                                            

                                 x = ________

                        iii.   x = ( 3 * 9 * ( 3 + ( 9 * 3 / 3 ) ) )                                                                                                    

                                 x = ________

2. Write a Python program that inputs three (3) integers to IDLE from the keyboard and prints the sum, average, product, smallest and largest of these numbers. For this exercise you may assume the user does NOT enter any duplicate values. The interactive screen dialogue should look something like this (user input is shown in bold):

Input three different integers separated by <enters>:

13

27

14

                                    Sum is 54

                                    Average is 18

                                    Product is 4914

                                    Smallest is 13

                                    Largest is 27

3. Write a Python program in IDLE that asks for the radius of a circle and prints the circle’s diameter, circumference, and area. Import the math library for p. Do the calculations for diameter, circumference and area in the output statements. You do NOT need variables for holding your calculated values of diameter, circumference, or area. Just place the appropriate expression as an argument to the print() function.

4. Write a Python program in IDLE that asks for an integer and determines and prints whether it is odd or even. (Hint: Use the modulus operator (%). An even number is a multiple of 2 and any multiple of 2 leaves a remainder of zero (0) when divided by 2).

Discussion:

In addition to the documentation requirements specified in lab 1, first write the entire program in pseudocode as comments. When necessary place a comment to the right of complicated lines to clarify your code to the reader. Further, comments should not merely repeat what is obvious from a program statement. For example, avoid what follows. This statement below adds nothing to understanding what the statement does or what its purpose is within the program:

                        Sum = Sum + 1   # Add 1 to Sum ß A totally worthless comment!

Deliverable(s):

Your deliverable should be a Word document with screenshots showing the sample code you have created, and discuss the issues that you had for this project related to AWS and/or Python IDE and how you solved them.

Turn in your source code listings for the programs developed above. Include screen shots of the results from running the programs you developed for three (3) sets of test data (for each program). Choose your test cases carefully so they reflect good values to test all aspects of your solutions.

Rewrite your most recent high scores program in C++ so that each name/score pair is stored in a struct named Highscore. Except as noted below, this new program will continue to meet all of the requirements of your most recent high scores program. Your new program should meet the following additional requirements:

1. The Highscore struct should have two fields:
   • an int named score
   • and a char array named name. The char array should have 24 elements, making the maximum length of the name 23.
2. The data should be stored in a single array, a dynamically allocated array of Highscore structs.
3. Your program should use three functions that accept the array of Highscore structs:

   void readData(Highscore scores[], int size)
   void sortData(Highscore scores[], int size)
   void displayData(const Highscore scores[], int size)
   

4. You may use any sort algorithm, but I would recommend using the selection sort from lesson 9.6. Don't use C++'s sort() function, but you can use the swap() function.
5. Note that when you swap your array elements, you can swap the entire struct. You don't need to swap the name and the score separately.
6. You may assume that the user enters names that are 23 characters or less.
7. Be sure to declare your struct above your prototypes, since the word "Highscore" appears in your prototypes.

Please help!! Heres my code below from the previous assignment that it asks for thank you!

#include

#include <iostream>

#include <cstdlib>

using namespace std;

void readData(int *scores, string *names, int n);

void sortData(int *scores, string *names, int n);

void displayData(int *scores, string *names, int n);

int main()

{

int n;

   cout<<"How many scores will you enter?: ";

   cin>>n;

int *scores = new int[n];

string *names = new string[n];

readData(scores, names, n);

sortData(scores, names, n);

displayData(scores, names, n);

delete [] scores;

delete [] names;

return 0;

}

void readData(int *scores, string *names,int n)

{

for (int i=0; i<n; i++)

{

cout<<"Enter the name for score #"<<(i+1)<<": ";

cin>>names[i];

cout<<"Enter the score for score #"<<(i+1)<<": ";

cin>>scores[i];

}

}

void sortData(int *scores, string *names, int n)

{

int i, j, size_t;

for (i = 0; i < n-1; i++)

{

size_t = i;

for (j = i+1; j < n; j++)

if (scores[j] > scores[size_t])

size_t = j;

string tempName = names[size_t];

names[size_t] = names[i];

names[i] = tempName;

int tempScore = scores[size_t];

scores[size_t] = scores[i];

scores[i] = tempScore;

}

}

void displayData(int *scores, string *names, int n){

   cout<<"Top Scorers: "<<endl;

   for(int i=0; i<n;i++){

   cout<<names[i]<<" : "<<scores[i]<<endl;

   }

}

For this week’s assignment, you will write a program class that has two subroutines and a main routine. The program should be a part of the ‘Firstsubroutines’ class and you should name your project Firstsubroutines if you are using Netbeans.

Your program must prompt the user to enter a string. The program must then test the string entered by the user to determine whether it is a palindrome. A palindrome is a string that reads the same backwards and forwards, such as "radar", "racecar", and "able was I ere I saw elba". It is customary to ignore spaces, punctuation, and capitalization when looking for palindromes. For example, "A man, a plan, a canal. Panama!" is considered to be a palindrome.

To determine whether a string is a palindrome, you can: convert the string to lower case; remove any non-letter characters from the string; and compare the resulting string with the reverse of the same string. If they are equal, then the original string is considered to be a palindrome.

Here’s the code for computing the reverse of str:

  String reverse;

  int i;

  reverse = "";

  for (i = str.length() - 1; i >= 0; i--) {

        reverse = reverse + str.charAt(i);

  }
  

As part of your assignment, you must write a static subroutine that finds the reverse of a string. The subroutine should have one parameter of type String and a return value of type String.

You must also write a second subroutine that takes a String as a parameter and returns a String. This subroutine should make a new string that is a copy of the parameter string, except that all the non-letters have been omitted. The new string should be returned as the value of the subroutine. You can tell that a character, ch is a lower-case letter by testing if (ch >= 'a' && ch <= 'z')

(Note that for the operation of converting str to lower case, you can simply use the built-in toLowerCase subroutine by saying: str = str.toLowerCase();)

You should write a descriptive comment before each subroutine, saying what it does.

Finally, write a main() routine that will read in a string from the user and determine whether or not it is a palindrome. The main routine should use The program should print the string converted to lower case and stripped of any non-letter characters. Then it should print the reverse string. Finally, it should say whether the string is a palindrome. (Use the two subroutines to process the user's string.) For example, if the user's input is "Hello World!", then the output might be:

    stripped: helloworld
    
    reversed: dlrowolleh
    
    This is NOT a palindrome.
    
    and if the input is "Campus motto: Bottoms up, Mac!", the output might be:
    
    stripped: campusmottobottomsupmac
    
    reversed: campusmottobottomsupmac  

    This IS a palindrome.
  

You must complete your program, test, debug, and execute it. You should test two different cases, one that is a palindrome and another one that is not a palindrome. You must submit your java code file (preferably by cut and paste the code into the assignment dialog box). The output of your program must be captured by either copying the content in the output window and pasting it into the assignment dialog box or by capturing the image of the screen which contains the output of your java program or the output and submitting this with your assignment as an attachment. In windows you can capture a screen shot with the Ctrl Alt and Print Screen key sequence. This image can then be pasted into a Word, WordPad, or OpenOffice document which can be submitted with your assignment.

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do any hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

1. A team of researchers has developed a new weight loss supplement. They want to know if patients who use the new supplement for four weeks lose any weight. The supplement has some minor side effects including mild headaches and achiness. If the researchers obtain evidence of weight loss they will proceed to produce the supplement commercially and sell it for a large profit. If they do not obtain evidence of weight loss they will end the project. [70 points]

A. State the null and alternative hypotheses that the researchers should test. Use m_d to denote the mean weight loss computed as beginning weight minus final weight.

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?

D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.

E. If you were working with this research team, what alpha level would you use? Explain your reasoning.

Assume that the research team completes this study with a sample size of 500 and finds a mean weight loss of 0.475 pound with a standard deviation of 3.978 pounds. Their p-value is 0.0039

F. Using the alpha level you selected in part E, are their results statistically significant? Explain why or why not.

G. Are their results practically significant? Explain why or why not.

2. The STAT 200 course coordinator wants to estimate the proportion of all online STAT 200 students who utilize Penn State Learning’s online tutoring services by either attending a live session or viewing recordings of sessions. In a survey of 80 students during the Fall 2018 semester, 29 had utilized their services. She used bootstrapping methods to construct a 95% confidence interval for the population proportion of [0.263, 0.475]. Use this information to address the following questions. [30 points]

A. Supposed the coordinator decides that she wanted to conduct a hypothesis test instead. She wants to know if the proportion who utilize Penn State Learning’s online tutoring services is different from 0.25. What would be the appropriate null and alternative hypotheses?

B. Based on the 95% bootstrap confidence interval, would you expect the coordinator to reject or fail to reject the null hypothesis from part A at the 0.05 alpha level? Do NOT conduct the hypothesis test; use the confidence interval given in the question. Explain your reasoning.

C. Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference.

Writing Assignment #1 Set of Instructions for a Website Summary of the Assignment: • Task: In this assignment, you will write a set of instructions that explain how to accomplish a task on a website. • Length: There is no minimum or maximum word count. However, your instructions must have 6 or more steps. More information on the number of steps is provided below. • Graphics: You must include at least one graphic for each step. o at least 6 graphics should be integrated into your set of instructions o all graphics should be screen captures of the website you are demonstrating o all graphics should be labeled • The first step of the set of instructions should start at the url of the website. o Do not start the instructions by telling the user to turn on his or her computer or to open up a particular web browser. You should assume the user knows that he or she needs to have a computer, needs to turn it on, and needs to use a web browser. You should start by directing the user to start at the url of the website on which the task is going to take place. Brief Description and Strategies to Follow: Please keep in mind the following principles when writing this assignment: • You must provide instructions on how to accomplish a task on a website. Some examples of topics are the following. (Keep in mind that you may select your own topic. These are just examples to help you consider various topics.) o how to check your balance in your checking account online o how to perform a function in your class in LEO o how to find and borrow a book on your local public library’s website o how to pay a fee on the website for the Motor Vehicle Association in Maryland (or the equivalent for your state) o how to change your credit card information on Amazon’s website • You must have at least 6 steps. • Each step is to be numbered and is to begin with an imperative verb, as the resources in the class indicate. • Every step will include a picture or graphic to help the reader follow the instructions. Sections to Include in Your Set of Instructions: The set of instructions will include the following sections: • Title Page • Overview or Introduction with background information about why a user would want to accomplish the task you are describing. • Instructions o number all of the main steps, as the resources for the class indicate o provide a graphic for steps of the instructions that need a graphic ▪ all graphics will be screen captures of the website. ▪ all graphics should be labeled Helpful Guides and Resources: • Chapter 10 from Tebeaux and Dragga, which is available in the e-reserves section of the class, is a helpful document to review as you begin this assignment. • The Tech Writing Handbook by Dozuki, which is one of the resources listed in our class, has an appendix that provides tips in writing instructions and incorporating graphics into instructions. • The Mayfield Handbook, which is also one of the resources listed in our class, features excellent tips on writing instructions. o Section 2.8.3 of the handbook, Instructions and Procedures, will be particularly helpful. • Some sample sets of instructions written by previous students in WRTG 393 are provided

Question

Many theorists believe that people have an innate predisposition to learn language. Three of the following provide sources of evidence that these theorists use to support their belief. Which one is not used to support an inherited predisposition to learn language?

Group of answer choices

Children develop increasingly larger and more sophisticated vocabularies as they grow older.

Most languages have certain characteristics in common, such as similar ways of forming negatives.

Children sometimes learn a language more easily when they are exposed to it at a young age.

People in the same community learn the same language despite very different experiences with that language.

Question

Maureen vehemently denies that trees are plants. Her understanding of what a plant is reflects which of the following errors?

Group of answer choices

a pragmatic error

undergeneralization

overgeneralization

overregularization

Question

Knowing which word combinations are grammatically correct reflects knowledge of:

Group of answer choices

Semantics

Context

Generalization

Syntax

Question

Which one of the following sentences reflects overregularization in a child's speech? The words in question are underlined.

Group of answer choices

I ain't going to school today.

Are you gonna go on the field trip?

He don't know anything.

The sheeps are in the meadow.

Question

LaWanda understands that a single sentence can sometimes be interpreted in two or more ways. For example, she realizes that the sentence "I know more beautiful women than Miss America" has two possible interpretations: "I know women who are more beautiful than Miss America is" or "I know more beautiful women than Miss America knows." LaWanda's appreciation for the double meanings of some sentences reflects:

1. Overgeneralization
2. Metalinguistic awareness
3. Pragmatics
4. Expressive language

Group of answer choices

Expressive language

Overgeneralization

Pragmatics

Metalinguistic awareness

Question

Based on the textbook's discussion of bilingualism and bilingual children, three of the following statements are true. Which one of the statements is not necessarily true?

Group of answer choices

Bilingualism is sometimes the result of living in a household in which two languages are spoken regularly.

Learning a second language promotes greater metalinguistic awareness.

Children who learn a second language in addition to their native tongue tend to have a more positive attitude toward people who speak that second language.

Children who learn two languages before the age of four are likely to master less of each language than they would if they learned only one.

Question

Three of the following statements accurately describe the diversity we are likely to see in students' cognitive development. Which statement is inaccurate?

Group of answer choices

Rehearsal is more commonly observed in children who live in developing countries than in children who live in highly urbanized and industrialized ones.

When eighth graders are asked to separate and control variables in a problem about fishing, those who have often fished with family or friends will be more successful than students who have never fished.

Students with physical and sensory challenges may have less general knowledge of the world, limiting their ability to relate new experiences to things they already know.

Some children in a first-grade classroom may show concrete operational thought, whereas others may show signs of preoperational thought.

Chapter 6: Normal Probability (These problems are like the problems in Section 6.2). Using a Normal Distribution to find probabilities: Use the table E.2 in your text. Draw a sketch and indicate what probabilities (E.g. P (X<3 and X>10) for what is required for each part of the problem. To make sketches copy and paste into Word for the areas under the bell-curve you have the NormalSketch.ppt powerpoint slide in the Resources  Handout area on Laulima, The main point of providing a sketch is to give you a visual idea of what your solution will be. 2. Do problem (6 points) Remember, you need the sketches to get credit. You order and manage the medications in the Pharamacy for Queens hospital. The CEO is concerned because the hospital is ordering and stocking medicine with short shelf lives and its not being used and thrown away. There is a medicine called Harvoni that is used for Hepatitis the cost of a treatment is $95,000 and the shelf life for the medicine is 12 weeks. Last year s significant amount of this medicine was disposed because of the short shelf life: How many treatments should you order? For this question the mean (μ) was 20, the standard deviation (σ) was 5, skewness was .06 and kurtosis was - .27. a. You can find the probabilities for this problem assuming a normal (bell-shaped) curve. Why is it OK for this particular situation? b. What is the probability that you will use no more than10 treatments in a given week? c. What is the probability that will use more than 36 treatments in a given week? d. Would using more than 36 treatments in a week be an outlier for this data set? e. You expect touse μ harvoni each day. Because of the variability you will actually sell more or less each day. To understand this, find out how many less or more than μ you expect to sell 80% of the time. That is, find two values equal distance from the mean such that 80% of all values fall between them. Specifically find what number of x Harvoni where 80% of the values fall between μ-x and μ+x f. You can only have a fixed amount of amount of treatments on hand to sell every week. As in (e) you know you will surely use more or less than μ treatments each week. If you run out of treatments, your patients will die. But if you order too many treatments they will go bad and you will have to throw them out so you are willing to sell out occasionally. How many treatments must you have on hand to sell if you wanted to ensure you do not runl out more than 5% of the time? (This is called having a 95% service level) g. The z-value for having a given service level is called the safety-factor. Explain what this factor does in terms of μ and σ for the 95% service level you found in (f). What if you wanted to only have a 50% service level? What about 40% service level?