The document provides examples and step-by-step instructions for conducting linear regression analyses in Minitab. It discusses how to find confidence intervals for slopes, interpret regression results, make predictions based on regression equations, and conduct hypothesis tests regarding the significance of regression slopes. For example 4, the null hypothesis is that the slope β1 equals 0, indicating crossword puzzle success and jelly beans consumed are not linearly related, while the alternative is that β1 does not equal 0, meaning they are linearly related. The t-statistic is 1.93490422105 and the p-value is 0.075, so the null cannot be rejected at the 0.10 significance level.
This presentation provides help on numbers 13, 15 and 19 on the Week 7 Homework. This contains hypothesis testing examples for 1 Sample z, 1 Sample t and 1 proportion.
This presentation provides help on numbers 13, 15 and 19 on the Week 7 Homework. This contains hypothesis testing examples for 1 Sample z, 1 Sample t and 1 proportion.
This presentation describes choosing the right options in Minitab for distributions related to the "tail" of the distribution. I cover Binomial, Poisson and the Geometric Distributions.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
This presentation describes choosing the right options in Minitab for distributions related to the "tail" of the distribution. I cover Binomial, Poisson and the Geometric Distributions.
Chapter 8 Confidence Interval Estimation
Estimation Process
Point Estimates
Interval Estimates
Confidence Interval Estimation for the Mean ( Known )
Confidence Interval Estimation for the Mean ( Unknown )
Confidence Interval Estimation for the Proportion
Crazy Futures aka Rx for Leadership Scotomas (why plausibility is maladaptive)Wendy Schultz
Short slidedeck on overcoming mental boundaries and expanding conceptual horizons in considering what possible futures may emerge, as a means to avoiding decision blindspots and black elephants / black swans.
Criação do projeto de design editorial para um livro atrativo visualmente, com estética e direção de arte bem trabalhadas, que aborda a vida e a obra do cineasta Tim Burton. (Enfoque no trabalho da estética do produto e não de seu conteúdo literário.)
PA 1c. Decision VariablesabcdCalculated values0.21110.531110.09760.docxgerardkortney
PA 1c. Decision VariablesabcdCalculated values0.21110.531110.09760.16019TotalObjective Function0.860.940.930.850.90772Constraints1111110.774-0.094-0.093-0.0850.09077>=0-0.0860.846-0.093-0.0850.40847>=0-0.086-0.0940.837-0.0851.90E-17>=0-0.086-0.094-0.0930.7650.04539>=00.94-2.790.22693>=00.86-1.86-2.00E-16>=0-0.129-0.141-0.13950.72256.90E-17>=0
a.
Let the weights be a, b, c and d to midterm, final, individual assignment and Participation respectively.
Korey would like to maximize the course grade. Therefore the course grade (Maximization):
=0.86a + 0.94b + 0.93c + 0.85d
Restrictions to course grade working: a+b+c+d=1
The weights must be non-negative, Non negativity constraints: a, b, c, d ≥ 0
The four components for each should determine 10% of the sum of the grade at least.
0.86a ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.86a ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.774a – 0.094b – 0.093c -0.085d ≥ 0
0.94b ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0846b ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.846b – 0.086a – 0.093c – 0.085d ≥ 0
0.93c ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.93c ≥ 0.086a +0.094b +0.093c + 0.085d
0.837c – 0.086a – 0.094b – 0.085d ≥ 0
0.85d ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.85d ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.765d – 0.086a – 0.094b – 0.093c ≥ 0
Here it is three times the particular assignment grade.
0.94b ≥ 3(0.93c)
0.94b ≥ 2.79c
0.94b – 2.79c ≥ 0
Midterm grade must count at least twice as much as the individual assignment score.
0.86a ≥ 2(0.93c)
0.86a ≥ 1.86c
0.86a – 1.86c ≥ 0
The presence of the grade should be less than the 15% of the whole grade.
0.85d ≤ 0.15(0.86a + 0.94b +0.93c +0.85d)
0.85d ≤ 0.129a + 0.141b +0.1395c + 0.1275d
0.7225d – 00.129a – 0.141b – 0.1395c ≥ 0
b.
The complete optimization model is Course grade (Maximization):
= 0.86a + 0.94b + 0.93c + 0.85d
a+b+c+d=1
0.774a – 0.094b - 0.093c – 0.085d ≥ 0
0.846b – 0.086a – 0.093c – 0.085d ≥ 0
0.837c – 0.086a – 0.094b – 0.085d ≥ 0
0.765d – 0.086a – 0.094b – 0.093c ≥ 0
0.94b – 2.79c ≥ 0
0.86a – 1.86c ≥ 0
0.7225d – 0.129a – 0.141b – 0.1395c ≥ 0
c.
Therefore midterm weights should be 21%, final weights 53%, individual assignment 10%, Participation should be 16%.
The maximum course grade is 90%.
PA 5b.Rosenberg Land DevelopmentDataOneTwoThreeBedroomBedroomBedroomUnitUnitUnit1BR2BR3BRAvailableConstruction cost$450,000$600,000$750,000$180,000,000Total units325Profit/ unit$45,000$60,000$75,000Minimum15%25%25%ModelTotalUnits Build4067162270Minimum406767Construction cost$18,202,247$40,449,438$121,348,315$180,000,000Contribution in profit$1,820,225$4,044,944$12,134,831$18,000,000c.ModelTotalUnits Build4981195325Minimum498181Construction cost$21,937,500$48,750,000$146,250,000$216,937,500Contribution in profit$2,193,750$4,875,000$14,625,000$21,693,750
a.
1BR = number of one bedroom units produced
2BR = number of two bedroom units produced
3BR = number of three bedroom units produced
Maximize Total Profit = $45,000 (1BR) + $60,000 (2BR) + $75,000 (3BR)
(1BR) + (2BR) + (.
Math 131 he goal of this lab is to find descriptive statistics/tutorialoutletHussanz
FOR MORE CLASSES VISIT
tutorialoutletdotcom
MATH 131
Lab 3 8/16 The goal of this lab is to find descriptive statistics for your quantitative data.
Part 1: V2, Quantitative Data
(3 points) Use the list of all 40 numbers from Lab 1, column V2 for this part of the lab.
Help on funky proportion confidence interval questionsBrent Heard
This presentation provides an alternate way of getting confidence intervals for proportions. We have at least one problem in Week 6 where this applies. Rather than using Minitab, I have an Excel template that will help. Instructions on obtaining the file are at the end of the presentation.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
1. MATH 533 WEEK 6 - MORE
HELP
B. Heard
These charts may not be
posted or shared without
my permission. Students
may download a copy for
personal use.
2. MATH 533 WEEK 6 - MORE HELP
Example 1 – The results for the output of a certain component are
tracked consistently to make sure that that the component performs
as advertised. Suppose the component’s manufacturer wants to use
simple linear regression to predict the output in volts (y) from the
setting on one of it’s machines (x). Find a 90% confidence interval for
the true slope of the line and interpret what the results mean.
Data on following page.
Also, remember the general form of the equation is
y = β0 + β1x + ε
3. MATH 533 WEEK 6 - MORE HELP
Batch
Output/Volt
s
Setting
1 3.3 100
2 3.6 108
3 4.1 138
4 4 90
5 3.9 104
6 4.1 95
7 3.9 113
8 3.7 149
9 3.7 119
10 4 92
11 3.5 290
12 3.7 136
13 4 184
14 3.6 139
15 3.4 164
16 3.4 263
17 3.9 151
18 3.6 144
19 3.8 108
20 3.4 143
21 4 113
22 3.9 100
23 3.9 125
24 4 121
25 3.6 137
Remember the output in volts is (y) and the setting is (x).
4. MATH 533 WEEK 6 - MORE HELP
First copy and paste data into Minitab…
5. MATH 533 WEEK 6 - MORE HELP
Now go to Stat >> Regression >> Regression (remembering which
one is x and which one is y)
6. MATH 533 WEEK 6 - MORE HELP
I get my results in the session window…
7. MATH 533 WEEK 6 - MORE HELP
What I will need now are the following two things…
The slope (β1) and the standard error (sβ1)… I have them both as seen below
8. MATH 533 WEEK 6 - MORE HELP
Now I will need my value for tα/2, Go to Graph >> Probability Distribution Plot,
click View Probability, then Ok
9. MATH 533 WEEK 6 - MORE HELP
Set distribution to t and your degrees of freedom to your sample size
minus 2. (In this case 25-2 = 23
10. MATH 533 WEEK 6 - MORE HELP
Click the Shaded Area Tab, Probability Radial Button, Both Tails
button and then enter 0.10 for probability (1 – your confidence)
11. MATH 533 WEEK 6 - MORE HELP
After clicking OK, you will see that your t value is 1.714
0.4
0.3
0.2
0.1
0.0
X
Density
-1.714
0.05
1.714
0.05
0
Distribution Plot
T, df=23
12. MATH 533 WEEK 6 - MORE HELP
Now I can easily get my confidence interval by using…
(β1) +/- (tα/2)(sβ1) (My Betas should have rooftops on them)
Let’s look at the results…
13. MATH 533 WEEK 6 - MORE HELP
(β1) +/- (tα/2)(sβ1)
(-0.00223) +/- (1.714)(0.0009321) = (-0.0038, -0.0006) Rounded to 4 Decimals
0.4
0.3
0.2
0.1
0.0
X
Density
-1.714
0.05
1.714
0.05
0
Distribution Plot
T, df=23
14. MATH 533 WEEK 6 - MORE HELP
Interpret results
The y-intercept would have no practical interpretation because a
machine setting of 0 is outside the range of the sample data.
However, the slope does have meaning, because for each additional
unit in setting, the output in volts is estimated to change by the value
of the slope.
15. MATH 533 WEEK 6 - MORE HELP
Example 2 – A study was done on the results of students quiz grades
based on the number of hours studied. 8 Different students were
examined. Based on the given data find the least squares line
relating score (y) to hours studied (x).
Student Score
Hours
Studied
1 88.5 30
2 88.3 27.6
3 86.3 25.3
4 76.9 23.4
5 87.2 28.9
6 90.4 34.8
7 75.6 21.8
8 85.7 26.1
16. MATH 533 WEEK 6 - MORE HELP
Copy Data into Minitab, then Go to Stat >> Regression >>
Regression
17. MATH 533 WEEK 6 - MORE HELP
Regression Equation is y = 53.627+1.147x ( to three decimals)
Note I used the
coefficients circled
because they gave me
the accuracy I needed.
18. MATH 533 WEEK 6 - MORE HELP
Interpretations
The y intercept has no meaning since 0 is not in the observed range
of study hours.
However, the slope does have meaning. For each hour increase in
study hours, the score is estimated to increase by the slope.
Remember that β0 is your y-intercept and β0 is your slope. My β’s should have
“rooftops” on them – You know a “^”…
19. MATH 533 WEEK 6 - MORE HELP
Predict the score of a student who studies 30 hours.
Just plug and chug.
y = 53.627+1.147x
Plug a 30 in for x
y = 53.627+1.147(30)
y = 88.037 (three decimals)
Always pay attention to the required accuracy (number of decimals)
20. MATH 533 WEEK 6 - MORE HELP
Example 3 – A study was done on ranking the total driving
performance of some really bad golfers like me. The method required
knowing the golfer’s average driving distance and driving accuracy
(shots in the fairway). In the study, they constructed a straight line
model relating driving accuracy (y) to driving distance (x). A Minitab
printout with prediction and confidence intervals for a driving
distance of x = 200 is shown below.Minitab Output
Predicted Values For New Observations
New
Obs Fit SE Fit 95% CI 95% PI
1 68.253 0.426
(42.265,
45.362)
(38.258,
49.956)
Values of Predictors for New
Observations
New
Obs
Distanc
e
1 200
21. MATH 533 WEEK 6 - MORE HELP
What is a practical interpretation of the results on the printout?
Well, we would say we are 95% confident that the actual driving
accuracy for a golfer driving the ball 200 yards is between the limits
of the prediction interval.
Key words: One golfer or in this case, “a golfer” goes with the
Prediction Interval
“All golfers” goes with the confidence interval. Don’t let them fool
you.
22. MATH 533 WEEK 6 - MORE HELP
What is the 95% confidence interval? 95% prediction interval?
Minitab Output
Predicted Values For New Observations
New
Obs Fit SE Fit 95% CI 95% PI
1 68.253 0.426
(42.265,
45.362)
(38.258,
49.956)
Values of Predictors for New Observations
New
Obs
Distanc
e
1 200
23. MATH 533 WEEK 6 - MORE HELP
Again, if you are interested in knowing the average driving distance
of
“All golfers” - Use confidence interval (You would be 95% confident
in this case)
“A single golfer” – Use prediction interval (You would be 95%
confident in this case)
24. MATH 533 WEEK 6 - MORE HELP
Example 4 – A study on the effect of jelly beans on working
crossword puzzles measured the crossword puzzle success (on a 30
point scale) and the number of jelly beans consumed before doing
the puzzle. On the basis of the information provided, the data shown
in the table on the next chart were obtained for 15 people who
participated in the study. Conduct a test to determine if the
crossword puzzle success (y) is linearly related to the number of jelly
beans consumed (x). Use α = 0.10
25. MATH 533 WEEK 6 - MORE HELP
Data for Example 3 Crossword Puzzle
Success
Jelly Beans
Consumed
18.8 49
19.3 49
19.8 52
19.1 53
20 53
20.3 53
19.2 56
17.4 58
18.7 58
20.3 58
20.8 59
21 60
20.9 62
21.3 62
20.5 61
26. MATH 533 WEEK 6 - MORE HELP
What would the correct null and alternative hypotheses be?
We are testing to see if they are linearly related, so they would be
H0: β1 = 0
Ha: β1 ≠ 0
27. MATH 533 WEEK 6 - MORE HELP
Find the test statistic and p value.
These can be tricky when you are not sure the number of decimals
(accuracy) you will need. I’m going to show you how to get more
accuracy if you need it.
28. MATH 533 WEEK 6 - MORE HELP
Get your data into Minitab
29. MATH 533 WEEK 6 - MORE HELP
Use Stat >> Regression >> Regression
30. MATH 533 WEEK 6 - MORE HELP
Session Window
Here is the test statistic t, and
the p value.
BUT
BUT
BUT
Go to next chart…
31. MATH 533 WEEK 6 - MORE HELP
What if they want the t value to three decimal places? Easy, watch…
t is given as 1.93 which is correct, but
to only two decimal places. The
testing software should be such that a
little tolerance is there, but to get more
accuracy just divide the Coef by the SE
Coef. In other words, look just to the
left of the 1.93 and divide 0.11414 by
0.05899
0.11414/0.05899 = 1.93490422105
blah blah
So, if they wanted three decimals, I
32. MATH 533 WEEK 6 - MORE HELP
So what is the appropriate conclusion?
Compare the p value 0.075 to alpha of 0.10.
If p is less Pless or Please Reject the null hypothesis, so we accept the
null that
β1 ≠ 0, so if it’s not zero, THEY MUST BE LINEARLY RELATED AT AN ALPHA OF 0.10
33. MATH 533 WEEK 6 - MORE HELP
This covers the hard stuff I think you will see on the quiz. Be
prepared…