This document provides an overview of regression analysis, including linear regression, multiple regression, and assessing assumptions. It defines regression as a technique for investigating relationships between variables. Simple linear regression involves one predictor and one response variable, while multiple regression extends this to multiple predictors. Key steps are outlined such as assessing the fit of regression models using R-squared, testing the significance of individual predictors, and ensuring assumptions of normality, linearity and equal variance are met. Examples are provided demonstrating how to evaluate these assumptions and interpret regression results.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
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.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
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.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
data science....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Broadly, plant tissue culture refers to “in vitro cultivation of all plant parts, whether a single cell, a tissue or an organ under aseptic conditions”. This is a technique with which “the plant cells, tissues or organs are on an artificial nutrient medium, either static or liquid, under aseptic and controlled conditions”.This presentation includes the requirements of PTC, various techniques of PTC
The Protein Data Bank (PDB) is a database for the three-dimensional structural data of large biological molecules, such as proteins and nucleic acids. This presentation deals with what, why, how, where and who of PDB. In this presentation we have also included briefing about various file formats available in PDB with emphasis on PDB file format
Probability distribution is a way to shape the sample data to make predictions and draw conclusions about an entire population because most improvement projects and scientific research studies are conducted with sample data rather than with data from an entire population. Probability distribution helps finding all the possible values a random variable can take between the minimum and maximum possible values
Chemistry Development Kit is a widely used open source cheminformatics toolkit, providing data structures to represent chemical concepts along with methods to manipulate such structures and perform variety of cheminformatics algorithms ranging from chemical structure canonicalization to molecular descriptor calculations and pharmacophore perception. The Chemistry Development Kit (CDK) is computer software, a library in the programming language Java, for chemoinformatics and bioinformatics. In this presentation a brief history of CDK, the various facilities provided by it, it's applications, and various analytical tools based on CDK such as CDK-Taverna, Bioclipse, PaDEL, Cinfony and, CDK extensions exist for KNIME are discussed.
Validation is the process of checking that your model is consistent with stereochemical standards i.e., validation is the process of evaluating reliability
In this presentation various aspects of validation are discussed
Metabolism is the set of life-sustaining chemical transformations within the cells of living organisms .The metabolome is the global collection of all low molecular weight metabolites that are produced by cells during metabolism, and provides a direct functional readout of cellular activity and physiological status. In this presentation i have given the list of various Metabolomic databases and metabolite databases. In addition to this there is a brief description about SMPDB and HMDB and BioTransformer
PHARMACOGNOSTICAL AND BIOLOGICAL ACTIVITY EVALUATION OF DECALEPIS HAMILTONIIAlichy Sowmya
Man requires basic necessities i.e. food, shelter and cloth. In addition to this attempts were made to reduce the severity of the disease or to cure different ailments. The biodiversity of natural resources like plants, animals, microbes, minerals and marine sources has served this need since time immemorial. Plants have played a crucial role in maintaining human health and improving the quality of human life for thousands of years. The World Health Organization has estimated that 80% of the earth’s inhabitants rely on traditional medicine for their health care needs, and most of this therapy involves the use of plants extracts or their active components.The use of the plants as medicine has been followed traditionally as trial and error and the effect of the plant medicine is being passed from generation to generation. It is orally familiar to the rustics.The plant is traditionally found to be useful for many ailments like haemorrhage, thirst,antimicrobial, urticaria, jaundice, gout, blood disorders and for diabetes. The literature review revealed that antibacterial activity was reported for leaves and roots of Decalepis aryalpathra.The genus Decalepis has been reported to posses different classes of compound mainly tannin,saponin, carbohydrate, fatty acid, flavanoids, alkaloids etc, which are responsible for antimicrobial and anthelmintic activity and also for treatment of various diseases.However, there is no scientific evidence to verify these claims. There is a dearth of reports on
pharmacognostical, antimicrobial and anthelminthic activity of Decalepis hamiltonii. In view of the above, the current study was designed to verify these indigenous claims and to provide basis for the rationale use of tuberous herb namely Decalepis hamiltonii (D. hamiltonii,Asclepiadaceae), as antimicrobial and antihelminthic drug.
SciFinder and its utility in Drug discoveryAlichy Sowmya
SciFinder Scholar® is a Z39.50 Windows-based interface that provides easy access to the rich and diverse scientific information contained in the CAS databases including Chemical Abstracts from 1907 onwards. SFS is an elegant search interface to six core chemical-related databases. Five of these databases are produced by CAS itself
Prescription Filling Record is the record of the original prescription and refill records. In this report, the various contents of the record , the procedures for dispensing the records and the procedures for the storage of the records have been discussed.
Information science is a multi disciplinary science with applications in a wide range of aspects. In this presentation there is a brief introduction to what is information science, how it orginated and characteristics of information science. It also covers the various definitions of information science.
Limitations of in silico drug discovery methodsAlichy Sowmya
In drug discovery there are various in silico approaches such as Virtual high throughput screening, Molecular docking, Homology modelling, QSAR, CoMFA, Molecular Dynamics, and Pharmacophore mapping. In this presentation various limitations of these approaches are given
Crimean Congo Hemorrhagic fever is a deadly infection of CCHFV. CCHFV is a biosafety level 4 virus. In this presentation the general introduction to the CCHF and CCHFV is given along with various computational drug design approaches for CCHF
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Data Centers - Striving Within A Narrow Range - Research Report - MCG - May 2...pchutichetpong
M Capital Group (“MCG”) expects to see demand and the changing evolution of supply, facilitated through institutional investment rotation out of offices and into work from home (“WFH”), while the ever-expanding need for data storage as global internet usage expands, with experts predicting 5.3 billion users by 2023. These market factors will be underpinned by technological changes, such as progressing cloud services and edge sites, allowing the industry to see strong expected annual growth of 13% over the next 4 years.
Whilst competitive headwinds remain, represented through the recent second bankruptcy filing of Sungard, which blames “COVID-19 and other macroeconomic trends including delayed customer spending decisions, insourcing and reductions in IT spending, energy inflation and reduction in demand for certain services”, the industry has seen key adjustments, where MCG believes that engineering cost management and technological innovation will be paramount to success.
MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
According to M Capital Group: “Specifically, the long-term cost-saving opportunities available from the rise of remote managing will likely aid value growth for the industry. Through margin optimization and further availability of capital for reinvestment, strong players will maintain their competitive foothold, while weaker players exit the market to balance supply and demand.”
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
From intelligent search and recommendations to automated data productisation and quotation, Opendatabay AI-driven features streamline the data workflow. Finding the data you need shouldn't be a complex. Opendatabay simplifies the data acquisition process with an intuitive interface and robust search tools. Effortlessly explore, discover, and access the data you need, allowing you to focus on extracting valuable insights. Opendatabay breaks new ground with a dedicated, AI-generated, synthetic datasets.
Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
3. “◉ Linear Regression is a supervised modeling technique for continuous data that generates a
response based on the set of input features.
◉ It is used for explaining the linear relationship between a single variable Y, called the response
(output or dependent variable), and one or more predictor (input, independent or explanatory
variables).
◉ It’s a simple regression problem if only a single variable X is considered, otherwise it takes the
form of a multiple regression problem, that is if more than one predictor is used in the model.
3
4. ◉ Statistical Modelling is the process of obtaining a
statistical model which adequately describes the
relationships between the variables involved
◉ The model: takes the form of a prediction equation - the
values of a dependent variable (DV) are predicted by a
set of independent variables (IV)
◉ Simplest model: simple linear regression
4
6. Simple Linear Regression
◉ SLR is investigating the linear relation between two variables
Y (DV) and X (IV or explanatory variable)
◉ “Linear”: used because the population mean of Y is
represented as a linear or straight-line function of X
◉ “Simple”: refers to the fact that there is only one independent
variable
◉ Examples:
• air quality and lung function
• medication dose and outcome of blood test
6
7. Explore the relationship Between Two
Continuous Variables
◉ Step 1: Scatterplot
Shape of scatterplot gives form of relation
• linear
• quadratic
• more complex
◉ Step 2: Correlation coefficient
Strength of linear relation given by correlation coefficient
• r: ranges from –1 to +1
• –1 : perfect negative linear relationship
• +1 : perfect positive linear relationship.
• 0 : no linear relationship.
7
9. ◉ Step 3: Simple linear regression
This is the population line.
• Y = dependent or response variable. Must be continuous.
• X = independent / predictor / explanatory variable or covariate
• α = population regression parameter / intercept: point where the
line crosses the vertical axis
• β = population regression parameter / slope: the change in the
mean value of Y for each increase of one unit in the value of X
• e = model error term e (residual)
= deviations between predicted values of Y and the actual values
of Y
Assumed normally distributed with mean 0 and
standard deviation
9
11. Objective of SLR
◉ Objective: to predict or estimate the value of DV Y
corresponding to a given value of IV X, thru the estimated
regression line
◉ Sample: the observed values are Xi and Yi, I =1,2,…n
◉ Build up: an estimated regression line using the sample. The
regression line from the observed data is an estimate of the
relationship between X and Y in the population
11
12. Estimated Regression Equation
◉ a = regression coefficient
= the estimate of the parameter α
= the intercept of the estimated regression line
= the value of Y where the line crosses the Y axis
◉ b = regression coefficient
= the estimate of the parameter β
= the slope of estimated regression line
= the change in the mean value of Y for each one unit increase in the value of X
12
13. Residual
◉ For any subject i, i = 1,2,3, …, n
◉ The original observed values are Xi and Yi
◉ For any given Xi , the ‘Y’ value given by the line is called the
predicted value and denoted by
◉ The residual ei is the difference between the predicted value
and the observed value
13
14. Least Squares Estimation
◉ Least squares estimation is the method of estimating the equation /
fitting the model to the data in an optimal way
◉ The sum of squares of the vertical distances of the observations from
the line are minimized
◉ Least squares estimation minimizes
14
16. Is X a significant predictor of Y
◉ The association between X and Y is given by the
regression coefficient for the slope
◉ A zero slope means X has no “impact” on Y
◉ whereas a large value indicates large changes in Y
when X changes
16
17. ◉ Denoted by R2
◉ Measures the goodness ‘fit’ of the model
◉ Assesses the usefulness or predictive value of the model
◉ Is interpreted as the proportion of variability in the observed
values of Y explained by the regression of Y on X
◉ E.g. R2 =71.9%, almost 72% of the variation in lung function
(FEV) is explained by the regression of FEV on height
◉ R2 =SSR/SST (eg., 78.34/109.01 = 0.719 =71.9%)
17
Coefficient of Determination
18. R2 and b
◉ The coefficient of determination R2 describes how well the
regression equation summaries the data
◉ The regression coefficient b gives the nature of the
relationship between X and Y the degree of change in Y for
certain changes in X
◉ Two data sets may have the same slope b but different R2
values and vise versa
18
21. Assumptions
1) The observations must be independent
2) The values of the dependent variable Y should be Normally distributed
(normality)
3) The variability (variance) of Y should be the same for each value of X -
homoscedasticity or constant variation
4) If X is continuous, the relation between X and Y should be linear (linearity)
Note
• X need not be a random variable nor have a Normal distribution
• In fact the assumptions need to hold for the residuals but can equivalently be tested for Y or the residuals
• A transformation of Y may be required
21
22. Assumptions - Strategies for testing
◉ Normality
• Test for Y values or for standardized residuals
• using 5 measures (histogram, Normal Q-Q plot, boxplot,
skewness and kurtosis statistics)
◉ Linearity
• Assess from scatterplot of X vs.Y
◉ Constant variation
• Plot of standardized residuals vs. X
• In plot of standardized residuals vs. X the points should scatter
randomly (without any pattern) and evenly (vertical spread the
same)
22
33. Multiple Regression
◉ Simple linear regression describes the linear relationship
between a dependent variable Y and a single explanatory
variable X
◉ Multiple regression is an extension to the case of one
dependent variable and two or more explanatory variables
33
34. Reasons for performing Multiple
regression
◉ Predictions on the basis of a number of variables will be better
than those based on only one explanatory variable
◉ When testing the effect of a primary variable of interest e.g.
treatment effect / exposure, one needs to account for all other
extraneous influences
• The need to ‘control’ or ‘adjust’ for the possible effects of
‘nuisance’ explanatory variables (known as confounders)
◉ The relationships may be complex e.g. variables may have
combined or synergistic effects on the dependent variable
34
35. Reasons for performing Multiple
regression
◉ It is almost always better to perform one comprehensive
analysis including all the relevant variables than a series of two-
way comparisons
• Reduce chances of increasing Type I error rate beyond 5%
• In multiple regression a linear model is fitted for the dependent
variable, which is expressed as a linear combination of the
independent variables
35
36. Importance of Predictors
◉ The regression coefficient bi represents the effect of that
independent variable on DV Y, after controlling for all
the other variables in the model
◉ The importance of each individual variable is tested by a
t test or an F test as for SLR
◉ Significance of an explanatory variable is dependent on
which other variables included in the regression model
◉ A confidence interval gives further information
36
37. Multiple regression models
◉ Multiple linear regression
• predictors all continuous and linearly related to the
dependent variable
◉ Analysis of covariance (ANCOVA)
• both continuous and categorical predictors
◉ Analysis of variance (eg. two-way ANOVA)
• predictors all categorical
◉ Polynomial regression
• quadratic or higher order terms included
37
38. Categorical predictors
◉ Association between a continuous DV Y and a categorical IV
X is assessed by comparing the mean Y values in each
category of X
◉ A reference category is chosen to compare the other
category/ies with
◉ The regression coefficient for a comparison represents the
difference in the mean for Y for the given category vs the
reference category
38
39. Assessing the fit of the model
◉ R2 measures usefulness or predictive value of model
◉ R2 is interpreted as the proportion of the total variability
explained by the model
◉ R2 increases in value as each additional variable is added to
the model
◉ adjusted R2 (preferred measure) takes into account the
number of explanatory variables included in the model
◉ E.g. R2 = 0.482 Radj2 =0.462
39
40. ◉ Also assess fit by inspection of standardized residuals
• If these follow a Normal distribution
• Any value
◉ Large residual: model does not fit well for that subject
◉ Some large residuals will occur by chance, many large
residuals are of concern s > 3 and < -3 are large
40
41. Assumptions of multiple regression
◉ The observations must be independent
◉ The relation between each continuous X and the dependent
variable should be linear
◉ The values of the dependent variable Y should have a Normal
distribution
◉ The variability of Y should be the same for any set of values of the
explanatory variables – homoscedasticity
41
42. How to assess assumptions
◉ Assessing the Normality of Y (or the standardized residuals)
• Obtaining scatterplots of Y (or the standardized residuals)
against each continuous X primarily to assess linearity
◉ Obtaining
• Levene’s test for Y (or the standardized residuals) (if
categorical predictors are included in the model) to assess
equal variance
• a plot of the standardized residuals against each X (if
continuous predictors are included in the model) primarily to
assess constant variation
42
43. Example - assess assumptions
◉ DV: FEV1
◉ Explanatory variables:
• Height (in cm’s)
• Gender (binary)
• Smoking status (3categories)
◉ Normality of FEV1 (5measures)
• skewness= -0.11,
• kurtosis -3 = -0.80
• Assumed
43
45. Constant variation:
◉ Constant variation:
• standardized residuals vs height (scatterplot): no clear pattern
◉ Assumed
45
46. Equality Variances
• Levenes’ Test (Robust): p = 0.937 >0.05,
• Assumed
46
Conclusion: All the assumptions are met
Note: the test could be done using standardized residuals
47. R Code for MLR
#loading of the data
data("mtcars")
#viewing the data
mtcars
head(mtcars)
names(mtcars)
#attach command is used in R so that we need not call the data
everytime
attach(mtcars)
#checking the realtionship between the variables
plot(mpg,cyl)
plot(mpg,disp)
plot(mpg,hp)
plot(mpg,drat)
plot(mpg,wt)
plot(mpg,qsec)
plot(mpg,vs)
47
plot(mpg,am)
plot(mpg,gear)
plot(mpg,carb)
#creating simple linear regression
#creating the multiple linear model
model <- lm(mpg~cyl+disp+hp+drat+wt+qsec+vs+am+gear+carb)
model
#checking the summary of the model
summary(model)
#various parameters to check the fitness of the model
#mean square error
sqrt(sum((model$residuals)^2)/21)
summary(model)
#hypothesis testing t-test
#test statistic is just the point estimate of the slope of the model divided by the standard error
of that coefficient/slope value
#example 1
tstat <- coef(summary(model))[3,1]/coef(summary(model))[3,2]
tstat
2*pt(tstat, 21, lower.tail=FALSE)
#example2
tstat2 <- coef(summary(model))[1,1]/coef(summary(model))[1,2]
tstat2
2*pt(tstat2, 21, lower.tail=FALSE)
summary(model)
48. 48
#F-test
summary(model)
#Coefficient Confidence Intervals
confint(model, level=.95)
#testing the various assumptions of the model
#1 checking whether the residuals are normally distributed or not
#histogram
resid<- model$residuals
hist(resid)
#quantile plot
qqnorm(resid)
qqline(resid)
#2 checking the homoscedasticity
plot(model$residuals ~ disp)
abline(0,0)
#residual analysis
plot(model)
#transformations
model1 = lm(mpg ~cyl+log(disp)+log(hp)+drat+wt+qsec+vs+am+gear+carb)
summary(model1)
plot(model1)
#reducing the model
#calling of library
library(MASS)
#running the AIC on intial model
stepAIC(model)
#running the AIC on the transformed model
stepAIC(model1)
#constructing new models with reduced variables
model2<-lm(mpg~qsec+wt+am)
summary(model2)
model6<-lm(mpg~log(disp)+gear+carb)
summary(model6)
#partial F-test
nestmodel = lm(mpg ~ wt + qsec + am)
anova(model,nestmodel)
#Multicollinearity
plot(mtcars)
#checking the correlation
cor(qsec, wt)
cor(am, wt)
cor(am, qsec)
#variance inflation factor
install.packages("car")
library(car)
vif(model2)
#Polynomial Model
plot(model2$residuals ~ model2$fitted.values, xlab = "Fitted Values", ylab = "Residuals")
abline(0,0)
quadmod = lm(mpg ~ qsec + I(qsec^2)+ wt + am)
plot(quadmod$residuals ~ quadmod$fitted.values, xlab = "Fitted Values", ylab = "Residuals")
abline(0,0)
summary(quadmod)
AIC(quadmod)
#Interaction Model
model3<-lm(mpg~qsec+wt*am)
summary(model3)
AIC(model3)
resid3<- model3$residuals
hist(resid3)
qqnorm(resid3)
qqline(resid3)
plot(model3$residuals ~ disp)
abline(0,0)
plot(model3)