It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
Topic: Regression
Student Name: Nayab
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
Topic: Regression
Student Name: Nayab
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Regression Analysis presentation by Al Arizmendez and Cathryn LottierAl Arizmendez
We present an overview of regression analysis, theoretical construct, then provide a graphic representation before performing multiple regression analysis step by step using SPSS (audio files accompany the tutorial).
Regression Analysis presentation by Al Arizmendez and Cathryn LottierAl Arizmendez
We present an overview of regression analysis, theoretical construct, then provide a graphic representation before performing multiple regression analysis step by step using SPSS (audio files accompany the tutorial).
MAGRAY- A MARTIAL KASHMIRI TRIBE/CASTE/RACEguest831335
MAGRAY-THE WARRIORS & MARTIALS OF KASHMIR:
Magray is a Martial Kashmiri tribe of Rajput origin. Magray sprung from Kashtri - un-Nassal Rajput. Kashtri-un-Nassal Rajput are one of the four classes of Hindus. Kashtri were people of ruling class having responsibility for the defence of the state. Ladhay Magray was the forefather of Magray tribe. Magres accepted Islam at the hand of Syed Ali Hamdani in thirteenth Century. The first person who entered in Kashmir and settled their belonged to Magray tribe thus making Magray tribe, the founders of Kashmir. Magray tribe ruled over Kashmir for seven hundred years. They invited Mughals to enter Kashmir in order to end disturbances in the valley. However, subsequently Mughals were defeated and pushed back by the Magray tribe. Magray tribe is settled all over the world with majority in Kashmir Valley. In spite of being SARDARS of the time, people of Magray tribe felt proud to be called as MAGRAY.
VILLAGES & TOWNS IN KASHMIR NAMED MAGRAY:
1. Magray Village District Bagh
2. Magray City Kuttan, Neelum valley, Muzaffarabad
3. Magray Hills Kanchikot, Rawalakot
4. Magray Abad, Barmang Rawalakot
5. Magray Gali Lipa Valley, Muzaffarabad
6. Magray Abad Attmaqam, Kel road,Neelum Valley
7. Magray Village Motarin, khaigala, Rawalakot
8. Kharl Magrayan District Bagh
9 Sardari Magrayan Neelum Valley Muzaffarabad
10. Magray village Marchkot Abbaspur
11. Bandian Magray Abbaspur.
MEANINGS OF MAGRAY:
Magray is an ancient word, Magray means,"TheMartials", "The Warriors", "Military and war like people". Magray is also spelled as Magrey, Magre and Magri, but the correct spelling is Magray. The plural of Magray is Magres.
BOOKS ON MAGRAY TRIBE:
All the historical books on Kashmir contain material on Magray tribe and their role in the history of Kashmir. Few of the historical Books are mentioned here for reference.
1. Magray in the Eyes of History By Sajid Latif Magray.
2. Magray A Warrior Kashmiri Tribe By Capt Ghulam Hussain Magray
3. Valley of Kashmir by Sir Walter Lirance.
4. Imperial Gazettier of India By Govt of India.
5. Tribes and Castes of Kashmir By Muhammad Din Folk.
6. Castes and Tribes of Poonch by Muhammad Din Folk.
7. History of Kasmir By Khawaja Azamey.
8. History of Kashmir By Muhammad Hassan.
9. History Kabeer Kashmir by Haji M.Mohiudin.
10. Raj Tarangi By Pandit Kahlan.
11. Tareekh-e-Kashmir by Professor Nazir Ahmed Tashna.
12. Kashmir in the Era of Muslim empires By Ghulam Hassan Khoyami.
13. Tareekh-e- Malkan By Dr Sadiq Malik.
14. Jalwa-e-Kashmir By Dr Sabir Afaqi
15. Baharistan-e-Shahi A Chronocle Mediaeval of Kashmir.
16. Magray - The Martials and Warriors of Kashmir by Sajiad Latif Magray.
17. Tareekh-e-Kashmir,Islami By Dr Sabir Afaqi.
18. Tareekh-e-Azmi By M.Azam.
19. Tribal geography of India Jamu and Kashmir By M. Bashir Magray.
20. A New History of India and Pakistan By Quyyam Abdul.
MAGRAY VILLAGES/TOWNS:
1. MAGRAY VILLAGE MOTARIN, RAWALKOT : This is a village comprising of about 400 houses, exclusively of the Magray Tribe. Road leading from Rawalkot to Tatrinote crossing point passes from this village. Few personalities of the village are: -a. Muhammad Din Magray. b. Subedar Muhammad Latif Magray. c. Sajjad Latif Magray. d. Rasheed Magray. e. Yaqoob Magray. f. Manzoor Magray. g. Sadique Magray. h. Dilpazir Magray. i. Muhammad Aamir Magray. j. Bashir Magray. k. Qayyum Magray. l. Yaseen Magray. m. Imran Yaseen marga. n. Shafi Magray. Akram Magray. p. Rafique Magray. q. Sajjad Magray. r. Muhammad Javed Magray. s. Kabir Magray. t. Kamran Magray. u.Saqib Magray
2. MAGRAY HILLS KANCHIKOT: This is a big village which starts from the Magray Market on Ali Sajal Road and goes to the Tolipeer, a prominent Hill top of Kashmir. Few personalities of the Magray Hills are:- a. Haji Aqal Hussain Magray. b. Tariq Magray. c. Ghulam Nabi Magray. d. Gulzar Magray. e. Havildar Yaseen margay. f. Sub
Titled, "These Are The Good Old Days" we explore the major changes that happened in 2016 that will fundamentally change how Revenue Managment for the Hospitality Industry will change.
For this assignment, use the aschooltest.sav dataset.The dMerrileeDelvalle969
For this assignment, use the aschooltest.sav dataset.
The dataset consists of Reading, Writing, Math, Science, and Social Studies test scores for 200 students. Demographic data include gender, race, SES, school type, and program type.
Instructions:
Work with the aschooltest.sav datafile and respond to the following questions in a few sentences. Please submit your SPSS output either in your assignment or separately.
1. Identify an Independent and Dependent Variable (of your choice) and develop a hypothesis about what you expect to find. (
note: the IV is a grouping variable, which means it needs to have more than 2 categories and the DV is continuous)
2. Run Assumption tests for Normality and initial Homogeneity of Variance. What are your results?
3. Run the one-way ANOVA with the Levene test & Tukey post hoc test.
a. What are the results of the Levene test? What does this mean?
b. What are the results of the one-way ANOVA (use notation)? What does it mean?
c. Are post hoc tests necessary? If so, what are the results of those analyses?
4. How do your analyses address your hypotheses?
Is concentration of single parent families associated with reading scores?
Using the AECF state data, the regression below measures the effect of the state's percentage of single parent families on the percentage of 4th graders with below basic reading scores.
%belowbasicread = β0 + β1x%SPF + u
Stata Output
1) Please write out the regression equation using the coefficients in the table
2) Please provide an interpretation of the coefficient for SPF
3) How does the model fit?
4) What is the NULL hypothesis for a T test about a regression coefficient?
5) What is the ALTERNATE hypothesis for a T test about a regression coefficient?
6) Look at the p value for the coefficient SPF.
a) Report the p value
b) How many stars would it get if we used our standard convention?
* p ≤ .1 ** p ≤ .05 *** p ≤ .01
image1.png
Two-Variable (Bivariate) Regression
In the last unit, we covered scatterplots and correlation. Social scientists use these as descriptive tools for getting an idea about how our variables of interest are related. But these tools only get us so far. Regression analysis is the next step. Regression is by far the most used tool in social science research.
Simple regression analysis can tell us several things:
1. Regression can estimate the relationship between x and y in their
original units of measurement. To see why this is so useful, consider the example of infant mortality and median family income. Let’s say that a policymaker is interested in knowing how much of a change in median family income is needed to significantly reduce the infant mortality rate. Correlation cannot answer this question, but regression can.
2. Regression can tell us how well the independent variable (x) explains the dependent variable (y). The measure is called the
R square.
Simple Tw ...
Two-Variable (Bivariate) RegressionIn the last unit, we covered LacieKlineeb
Two-Variable (Bivariate) Regression
In the last unit, we covered scatterplots and correlation. Social scientists use these as descriptive tools for getting an idea about how our variables of interest are related. But these tools only get us so far. Regression analysis is the next step. Regression is by far the most used tool in social science research.
Simple regression analysis can tell us several things:
1. Regression can estimate the relationship between x and y in their
original units of measurement. To see why this is so useful, consider the example of infant mortality and median family income. Let’s say that a policymaker is interested in knowing how much of a change in median family income is needed to significantly reduce the infant mortality rate. Correlation cannot answer this question, but regression can.
2. Regression can tell us how well the independent variable (x) explains the dependent variable (y). The measure is called the
R square.
Simple Two-Variable (Bivariate) Regression
Regression uses the equation of a line to estimate the relationship between x and y. You may remember back in algebra learning about the equation of a line. Some learned it as Y =s X + K or Y = mX + B. In statistics, we use a different form:
Equation 1: Y = B0 + B1X + u
Let’s define each term in the equation:
· Y is the dependent variable. It is placed on the Y (vertical) axis. In the example below, the dependent variable (Y) is the infant mortality rate.
· B0 is the Y intercept. B0 is also referred to as “the constant.” B0 is the point where the regression line crosses the Y axis. Importantly, B0 is equal to the
predicted value of Ywhen X=0. In most cases, B0 is does not get much attention for two reasons. First, the researcher is usually interested in the relationship between x and y. not the relationship between x and y at the single value of x=0. Second, often independent variables do not take on the value zero. Consider the AECF sample data. There are no states with low-birth-weight percentages equal to zero, so we would be extrapolating beyond what the data tell us.
· B1 is usually the main point of interest for researchers. It is the slope of the line relating x to y. Researchers usually refer to B1 as a slope coefficient, regression coefficient or simply a coefficient.
B1 measures the change in Y for a one-unit change in x. We represent change by the symbol ∆.
B1 =
· u is the error term. The error term is the distance between the regression line and the dots on the scatterplot. Think about it, regression estimates a single line through the cloud of data. Naturally, the line does not hit all the data points. The degree to which the line “misses” the data point is the error. u can also be thought of as
all the other factors that affect the infant mortality rate besides X. Importantly, we
assume that u is totally random given X.
The ...
Stuck with your Regression Assignment? Get 24/7 help from tutors with Phd in the subject. Email us at support@helpwithassignment.com
Reach us at http://www.HelpWithAssignment.com
Data Science - Part XII - Ridge Regression, LASSO, and Elastic NetsDerek Kane
This lecture provides an overview of some modern regression techniques including a discussion of the bias variance tradeoff for regression errors and the topic of shrinkage estimators. This leads into an overview of ridge regression, LASSO, and elastic nets. These topics will be discussed in detail and we will go through the calibration/diagnostics and then conclude with a practical example highlighting the techniques.
very detailed illustration of Log of Odds, Logit/ logistic regression and their types from binary logit, ordered logit to multinomial logit and also with their assumptions.
Thanks, for your time, if you enjoyed this short article there are tons of topics in advanced analytics, data science, and machine learning available in my medium repo. https://medium.com/@bobrupakroy
Linear regression is an approach for modeling the relationship between one dependent variable and one or more independent variables.
Algorithms to minimize the error are
OLS (Ordinary Least Square)
Gradient Descent and much more.
Let me know if anything is required. Ping me at google #bobrupakroy
Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest.
This 10 hours class is intended to give students the basis to empirically solve statistical problems. Talk 1 serves as an introduction to the statistical software R, and presents how to calculate basic measures such as mean, variance, correlation and gini index. Talk 2 shows how the central limit theorem and the law of the large numbers work empirically. Talk 3 presents the point estimate, the confidence interval and the hypothesis test for the most important parameters. Talk 4 introduces to the linear regression model and Talk 5 to the bootstrap world. Talk 5 also presents an easy example of a markov chains.
All the talks are supported by script codes, in R language.
Economics Assignment Sample Problems Set 6 with SolutionsHebrew Johnson
Don't let that tough economics assignment break you down for no reason. Have your economics assignments solved today by a team of expert tutors who will provide well explained and laid out solutions tailored to meet your requirements and ensure you submit perfect work on time. Get help 24/7 on economics homework by visiting https://www.economicshomeworkhelper.com/
2. Multiple Regression Model and Equation
What we learned in SLR, is also applicable in Multiple
Regression.
The multiple regression model simply extends SLR to include
more than 1 independent variable.
Hence we augment our simple linear model accomodate this:
y = β0 + β1x1 + β2x2 + ... + βpxp + ε
Additionally, since we still assume the expected value of ε to be
zero, we show the multiple regression equation as follows:
E(y) = β0 + β1x1 + β2x2 + ... + βpxp
3. Estimated Multiple Regression Equation
If β0, β1,...βp were known the equation on the previous slide
could be used to compute the mean value of y at given values
of x1, x2, ..., xp.
But we don't know them, so we need estimates b0, b1, ..., bp
Thus we arrive at the Estimated Regression Equation:
ŷ = b0 + b1x1 + b2x2 + ... + bpxp
5. Least Squares Method
To estimate our beta's, the objective is the same as SLR.
That is we seek to minimize the difference between our actual
dependent variable (y) and the prediction for that dependent
variable (ŷ).
Least Square Criterion: min Σ(yi - ŷi)2
In SLR, we had a relatively easy way to obtain our estimates.
In multiple regression, this is not so easy:
B = (X'X)-1X'Y
So we rely on statistical computing packages to do this for us.
6. Interpretation of Coefficients (β) in
Multiple Regression
Now that we have > 1 independent variables, we must be aware of the consequences of adding
multiple independent variables.
Notice from the example in Ch.15, that a b1 estimate computed with 1 independent variable (SLR)
will NOT be the same when additional independent variables are added.
In SLR we interpreted b1 as an estimate of the change in y for a 1 unit change in x.
In multiple regression, bi is an estimate of the change in y for a 1 unit change in xi when all other
independent variables are held constant. (For example, when they are all 0)
Take note also that now we can easily throw in as many independent variables as we want.
This will increase our explained variance, and our R2...So this is good, right??? Wrong.
While this may increase our ability to predict, it will also make our model increasingly complex.
Statistical power is achieved through accurate prediction with least amount of variables.
In the coming sections we will look at additional measures for 'model parsimony'...that is models
that 'do the most with the least'.
7. Model Assumptions
Our assumptions in multiple regression parallel those in
SLR. For emphasis, lets briefly review. (Also look at 15.11)
1. E(ε) = 0; Therefore E(y) = β0 + β1x1 + β2x2 + ... + βpxp
2. Var(ε) = σ2 and is the same for all values of x; Therefore the
variance about the regression line also equals σ2 and is the
same for all values of x.
3. The values of ε are independent; Therefore the values of ε
for any set of x values are not related to any other set of x
values.
4. ε is normally distributed random variable; Therefore y is
normally distributed.
8. Testing for Significance
In multiple regression significance testing carries slightly
different meaning than in SLR.
1. F-Test: Tests for a significant relationship between the
dependent variable and the set of all independent
variables. We refer to this as the test for overall significance.
2. If the F-Test shows overall significance, than we use the t-
test to check the significance for each of the independent
variables. We conduct the t-test on each of the independent
variables. We refer to the t-test as the test for individual
significance.
9. F-Test
In multiple regression, we test that none of the parameters are
equal to zero:
H0: β0 = β1 = ... = βp = 0
Ha: One or more of the parameters are equal to zero.
Remember that F = MSR/MSE.
And in multiple regression:
MSR = SSR/p
MSE = SSE/(n - p - 1)
And we reject H0 if our p-value < α
10. T-Test
Remember we test for each parameter.
For any βi:
H0: βi = 0
Ha: βi ≠ 0
t = βi/sbi
And we reject H0 if our p-value < α
11. Multicollinearity
This is essentially the correlation among independent variables.
We care about this because we want our independent variables to measure
significantly different things when predicting our dependent variable.
While in practice there is always some multicollinearity, we need to try and
eliminate as much as we can.
A simple test of multicollinearity is with the sample correlation (rx1x2) for any
two independent variables.
If the sample correlation exceeds .7 for any two independent variables we must
take measures to reduce multicollinearity, for example, removing one of the two
highly correlated variables from the model.
12. The End
Thats it for Ch. 15.
Hope you have recovered from Mardi Gras next time I see you!