Spss6 multiple regression
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Multiple regression can be used to explore the relationship between a continuous dependent variable and multiple independent variables. There are three main types of multiple regression: standard, hierarchical, and stepwise. Standard multiple regression involves entering all independent variables into the equation at once to determine how much variance in the dependent variable is explained collectively. The document then provides an example using standard multiple regression to predict perceived stress from measures of control (mastery and PCOISS), finding the model significantly predicts stress and that mastery and PCOISS each uniquely contribute to the prediction.
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Inferential AnalysisChapter 20NUR 6812Nursing Research
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Chapter 20
NUR 6812Nursing Research
Florida National University
Introduction - Inferential Analysis
We will discuss analysis of variance and regression, which are technically part of the same family of statistics known as the general linear method but are used to achieve different analytical goals
ANALYSIS OF VARIANCE
Analysis of variance (ANOVA) is used so often that Iversen and Norpoth (1987) said they once had a student who thought this was the name of an Italian statistician.
You can think of analysis of variance as a whole family of procedures beginning with the simple and frequently used t-test and becoming quite complicated with the use of multiple dependent variables (MANOVA, to be explained later in this chapter) and covariates.
Although the simpler varieties of these statistics can actually be calculated by hand, it is assumed that you will use a statistical software package for your calculations.
If you want to see how these calculations are done, you could try to compute a correlation, chi-square, t-test, or ANOVA yourself (see Yuker, 1958; Field, 2009), but in general it is too time consuming and too subject to human error to do these by hand.
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Several terms are used in these analyses that you need to be familiar with to understand the analyses themselves and the results. Many will already be familiar to you.
Statistical significance: This indicates the probability that the differences found are a result of error, not the treatment. Stated in terms of the P value, the convention is to accept either a 1% (P ≤ 0.01), or 1 out of 100, or 5% (P ≤ 0.05), or 5 out of 100, possibility that any differences seen could have been due to error (Cortina & Dunlap, 2007).
Research hypothesis: A research hypothesis is a declarative statement of the expected relationship between the dependent and independent variable(s).
Null hypothesis: The null hypothesis, based on the research hypothesis, states that the predicted relationships will not be found or that those found could have occurred by chance, meaning the difference will not be statistically significant.
Effect size: This is defined by Cortina and Dunlap as “the amount of variance in one variable accounted for by another in the sample at hand” (2007, p. 231). Effect size estimates are helpful adjuncts to significance testing. An important limitation, however, is that they are heavily influenced by the type of treatment or manipulation that occurred and the measures that are used.
Confidence intervals: Although sometimes suggested as an adjunct or replacement for the significance level, confidence intervals are determined in part by the alpha (significance level) (Cortina & Dunlap, 2007). Likened to a margin of error, the confidence intervals indicate the range within which the true difference between means may lie. A narrow confidence interval implies high precision; we can specify believable values within a narrow range ...
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2. It discusses the differences between samples and populations and how statistics like the mean and standard deviation from a sample can be used to make estimates about the overall population. Confidence intervals are presented as a way to indicate the reliability of sample estimates.
3. The document covers important statistical topics like effect sizes, which provide a standardized measure of the magnitude of an observed effect, and the differences between statistical and practical significance.
1. complete stats notes
1) Statistics is the science of collecting, analyzing, and drawing conclusions from data. It is used to understand populations based on samples since directly measuring entire populations is often impossible.
2) There are two main types of data: qualitative data which relates to descriptive characteristics, and quantitative data which can be expressed numerically. Common statistical analyses include calculating the mean, standard deviation, and using t-tests, ANOVA, correlation, and chi-squared tests.
3) Statistical analyses allow researchers to determine uncertainties in measurements, compare groups, identify relationships between variables, and assess whether observed differences are likely due to chance or a factor being studied. Key concepts include null and alternative hypotheses, p-values, and effect size.
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3. Testing if coefficients satisfy certain restrictions.
4. Testing the stability of a regression model over time using the Chow test.
5. Testing linear vs. log-linear functional forms using the MacKinnon-White-Davidson test.
The chapter outlines different statistical approaches like confidence intervals, F-tests, and t-tests to evaluate hypotheses about coefficients and models.
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We will discuss analysis of variance and regression, which are technically part of the same family of statistics known as the general linear method but are used to achieve different analytical goals
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Analysis of variance (ANOVA) is used so often that Iversen and Norpoth (1987) said they once had a student who thought this was the name of an Italian statistician.
You can think of analysis of variance as a whole family of procedures beginning with the simple and frequently used t-test and becoming quite complicated with the use of multiple dependent variables (MANOVA, to be explained later in this chapter) and covariates.
Although the simpler varieties of these statistics can actually be calculated by hand, it is assumed that you will use a statistical software package for your calculations.
If you want to see how these calculations are done, you could try to compute a correlation, chi-square, t-test, or ANOVA yourself (see Yuker, 1958; Field, 2009), but in general it is too time consuming and too subject to human error to do these by hand.
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Several terms are used in these analyses that you need to be familiar with to understand the analyses themselves and the results. Many will already be familiar to you.
Statistical significance: This indicates the probability that the differences found are a result of error, not the treatment. Stated in terms of the P value, the convention is to accept either a 1% (P ≤ 0.01), or 1 out of 100, or 5% (P ≤ 0.05), or 5 out of 100, possibility that any differences seen could have been due to error (Cortina & Dunlap, 2007).
Research hypothesis: A research hypothesis is a declarative statement of the expected relationship between the dependent and independent variable(s).
Null hypothesis: The null hypothesis, based on the research hypothesis, states that the predicted relationships will not be found or that those found could have occurred by chance, meaning the difference will not be statistically significant.
Effect size: This is defined by Cortina and Dunlap as “the amount of variance in one variable accounted for by another in the sample at hand” (2007, p. 231). Effect size estimates are helpful adjuncts to significance testing. An important limitation, however, is that they are heavily influenced by the type of treatment or manipulation that occurred and the measures that are used.
Confidence intervals: Although sometimes suggested as an adjunct or replacement for the significance level, confidence intervals are determined in part by the alpha (significance level) (Cortina & Dunlap, 2007). Likened to a margin of error, the confidence intervals indicate the range within which the true difference between means may lie. A narrow confidence interval implies high precision; we can specify believable values within a narrow range ...
Inferential AnalysisChapter 20NUR 6812Nursing Research
Inferential Analysis
Chapter 20
NUR 6812Nursing Research
Florida National University
Introduction - Inferential Analysis
We will discuss analysis of variance and regression, which are technically part of the same family of statistics known as the general linear method but are used to achieve different analytical goals
ANALYSIS OF VARIANCE
Analysis of variance (ANOVA) is used so often that Iversen and Norpoth (1987) said they once had a student who thought this was the name of an Italian statistician.
You can think of analysis of variance as a whole family of procedures beginning with the simple and frequently used t-test and becoming quite complicated with the use of multiple dependent variables (MANOVA, to be explained later in this chapter) and covariates.
Although the simpler varieties of these statistics can actually be calculated by hand, it is assumed that you will use a statistical software package for your calculations.
If you want to see how these calculations are done, you could try to compute a correlation, chi-square, t-test, or ANOVA yourself (see Yuker, 1958; Field, 2009), but in general it is too time consuming and too subject to human error to do these by hand.
IMPORTANT TERMINOLOGY
Several terms are used in these analyses that you need to be familiar with to understand the analyses themselves and the results. Many will already be familiar to you.
Statistical significance: This indicates the probability that the differences found are a result of error, not the treatment. Stated in terms of the P value, the convention is to accept either a 1% (P ≤ 0.01), or 1 out of 100, or 5% (P ≤ 0.05), or 5 out of 100, possibility that any differences seen could have been due to error (Cortina & Dunlap, 2007).
Research hypothesis: A research hypothesis is a declarative statement of the expected relationship between the dependent and independent variable(s).
Null hypothesis: The null hypothesis, based on the research hypothesis, states that the predicted relationships will not be found or that those found could have occurred by chance, meaning the difference will not be statistically significant.
Effect size: This is defined by Cortina and Dunlap as “the amount of variance in one variable accounted for by another in the sample at hand” (2007, p. 231). Effect size estimates are helpful adjuncts to significance testing. An important limitation, however, is that they are heavily influenced by the type of treatment or manipulation that occurred and the measures that are used.
Confidence intervals: Although sometimes suggested as an adjunct or replacement for the significance level, confidence intervals are determined in part by the alpha (significance level) (Cortina & Dunlap, 2007). Likened to a margin of error, the confidence intervals indicate the range within which the true difference between means may lie. A narrow confidence interval implies high precision; we can specify believable values within a narrow range ...
A researcher in attempting to run a regression model noticed a neg.docx
A researcher in attempting to run a regression model noticed a negative beta sign for an explanatory variable when s/he was expecting a positive sign based on theoretical considerations. What advice would you give to the researcher as to what is going on and what specific diagnostics would you look at? Explain conceptually and statisticallythe different ways you cancorrect for this problem.
Reason
One of the most common and important reasons for such situations is the existence of multicollinearity. Multicollinearity can happen if some of the independent variables are highly correlated to each other or to another variable that is not in the model.
Multicollinearity also has other symptoms such as
· Large variance for regression coefficients
· Non-significant individual coefficients while the general model is significant
· Change of marginal contributions depending on the variables in the model
· Large correlation coefficients in the correlation matrix of variables
It should however be noted that the general model can preserve its predictive ability and it is only the explanatory power that is lost
Before going to the solutions and measures the researcher can take it is wise to take a step back and see the underlying reason for the multicollinearity. An extreme case where two variables are identical gives the best understanding of problem
In this case we are trying to define y as a function of and while in reality . Therefore any linear combination of and is replaceable by infinite other linear combinations (ie )
It is simply understandable that while the y is predicted correctly in all the instances individual coefficients for and are meaningless.
Diagnosis
One of the most common diagnoses for multicollinearity is the variance inflation factor (VIF)
Where
And is the coefficient of multiple determination of regression of on other variables
The variance inflation factor therefore determines how much the variance of each coefficient inflates. when equals zero VIF equals 1 which suggests zero multicollinearity heuristic is that any value of VIF larger than 10 is alerting and a case of strong multicollinearity exists.
Solution
s
There are a few solutions for the multi Collinearity problem:
1- Ignoring the problem completely is possible for cases where we only care about the final model fit and prediction capability rather than individual coefficients and explanation power
2- Removing some of the correlated variables from the model, this can be justified since we can argue the effect of variable is however seen by similar highly correlated variables that are kept in the model
3- Principle component analysis (or any orthogonal transformation) can reduce the number of factors to a few orthogonal factors with no collinearity; however we should note that the interpretation of variables after a PC transformation is hard.
4- For cases where we intend to keep all the variables in the model without any major transformation, the Ridge regr.
Anova single factor
This document discusses a single factor analysis of variance (ANOVA) model. It defines ANOVA and explains that it allows comparison of three or more population means. The key assumptions of ANOVA are normal distributions and equal variances across populations. The document provides an example of using a single factor ANOVA to compare final exam scores from students in different teaching formats. Total variability is partitioned into between and within treatment variability, and average variability is measured using mean square values.
Analytic Methods and Issues in CER from Observational Data
UCSF researcher, Charles McCulloch, PhD, presents. View more related presentations and resources at http://accelerate.ucsf.edu/research/cer
Multinomial Logistic Regression.pdf
- Multinomial logistic regression predicts categorical membership in a dependent variable based on multiple independent variables. It is an extension of binary logistic regression that allows for more than two categories.
- Careful data analysis including checking for outliers and multicollinearity is important. A minimum sample size of 10 cases per independent variable is recommended.
- Multinomial logistic regression does not assume normality, linearity or homoscedasticity like discriminant function analysis does, making it more flexible and commonly used. It does assume independence between dependent variable categories.
Anova single factor
1) ANOVA is used to compare the means of more than two populations and determine if observed differences are due to chance or actual differences in the population means.
2) The document provides an example of using a one-way single factor ANOVA to analyze the effects of different teaching formats on student exam scores.
3) The ANOVA compares the between-treatment variability to the within-treatment variability using an F-test. If the between-treatment variability is significantly larger, it suggests the population means differ. In this example, the F-test showed no significant difference between the teaching formats.
Statistics in meta analysis
This document provides an overview of statistics used in meta-analysis. It discusses key concepts like odds ratios, relative risk, confidence intervals, heterogeneity, and fixed and random effects models. It also summarizes different types of meta-analyses including realist reviews, meta-narrative reviews, and network meta-analyses. Software for performing meta-analyses and potential pitfalls in systematic reviews are also briefly covered.
Chapter 12Choosing an Appropriate Statistical TestiStockph.docx
Chapter 12
Choosing an Appropriate Statistical Test
iStockphoto/ThinkstockLearning Objectives
After reading this chapter, you will be able to. . .
· understand the importance of using the proper statistical analysis.
· identify the type of analysis based on four critical questions.
· use the decision tree to identify the correct statistical test.
Here we are in the final chapter that will pull all prior chapters together. Chapters 1 to 3 discussed descriptive statistics while the latterchapters, 4 to 11, discussed inferential statistics. Each of the inferential chapters presented a statistical concept then conducted the appropriateanalysis to be able to test a hypothesis. The big question for students learning statistics is, "How do I know if I'm using the correct statisticaltest?" For experienced statisticians this question is easy to answer as it is based on a few criteria. However, to a student just learning statisticsor to the novice researcher, this question is a legitimate one. Many statistical reference texts include a guide that asks specific questionsregarding the type of research question, design, number and scales of measurement of variables, and statistical assumption of the data thatallows you to use an elegant chart known as a decision tree. Based on the answers to these questions, the decision tree is used to helpdetermine the type of analysis to be used for the research, thereby helping you answer this big question.
12.1 Considerations
To make the correct decisions based on the use of a decision tree, there are four specific questions that must be answered. These questions areas follows:
· What is your overarching research question?
· How many independent, dependent, and covariate variables are used in the study?
· What are the scales of measurement of each of your variables?
· Are there violations of statistical assumptions?
If you are able to answer these specific questions, then you will be able to determine the proper analysis for your study. These questions arecritically important, and if they cannot be answered, then not enough thought has gone into the research. That said, let us discuss each ofthese questions so that they can be considered and answered in the use of the decision tree.
What Is Your Overarching Research Question?Try It!
Derive your ownresearch question foryour Master's Thesisor DoctoralDissertation. Have a colleague orprofessor read it. What are theirthoughts or suggestions forimprovements?
Answering this question seems simple enough as all research has an overarching research questionthat drives the study, especially since this dictates the type of quantitative methodology. There arekey words in every research question that help determine the appropriate type of analysis. Forinstance, if the research question states, "What are the effects of job satisfaction on employeeproductivity?" the keyword is "effects" as in the cause and effect of job satisfaction (theindependent variable) on productivity (th ...
Quantitative_analysis.ppt
This document summarizes quantitative data analysis techniques. It discusses how to summarize data using simple statistics like means and standard deviations. It also covers effect statistics that summarize relationships between variables, such as slopes from regression. Statistical tests like t-tests and ANOVA are used to generalize sample results to populations and assess statistical significance. Precision is expressed using confidence intervals rather than just p-values. More complex models can also be reduced to these foundational analyses.
Binary OR Binomial logistic regression
Binary logistic regression can be used to model the relationship between predictor variables and a binary dependent variable. The document discusses using logistic regression to predict the likelihood of clients terminating counseling early based on gender, income level, avoidance of disclosure, and symptom severity. The full model was statistically significant and correctly classified 84.4% of cases. Avoidance of disclosure and symptom severity significantly predicted early termination, while gender and income level were not significant predictors.
What do youwant to doHow manyvariablesWhat level.docx
What do you
want to do?
How many
variables?
What level
of data?
Central
tendency
Describe
Median
Make
inferences
Univariate Bivariate Multivariate
Nominal Ordinal Interval/
Ratio
Central
tendency
Mode
Central
tendency
Mean
Dispersion Dispersion Dispersion
Variance,
Standard
deviation
Average,
Absolute
deviation
Range,
Index of
dispersion
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Learning Objectives
Understand the difference between dispersion and deviation.■■
Understand the range, variance, and standard deviation as measures of dis■■
persion.
Identify the proper measure of dispersion for analyzing data.■■
Explain how to calculate the range, variance, and standard deviation.■■
It is important to know the central value of a distribution, but it is just one character
istic of the distribution. It is also important to know how spread out the values are,
together with the central value, because it is possible to have two data sets with the
same measure of central tendency but with very different distributions. For example,
two tests were given, with the following results:
Test 1: 10 80 85 90 95 100
Test 2: 75 75 75 75 75 175
Each test has a mean of 75. The scores of test 1 range from 0 to 100, whereas all of
the scores for test 2 are 75. These distributions have the same mean but very differ
ent spreads of scores. If you did not know your score and had to choose which group
you were going to be in, you would want to know the spread of scores. If you are a
weak student, it might be better to go with the all75 group, whereas if you are a good
student, you would definitely want to go with the spread group. This is the reason it
is important to know the dispersion of the distribution together with the measure of
central tendency. Measures of dispersion measure how narrow or how spread out the
values are around the central value.
1 Deviation and Dispersion5-
Dispersion and deviation are largely synonymous. The only practical difference is
that deviation typically refers to the difference between a single value or case and the
measure of central tendency, whereas dispersion is used more to refer to the overall
difference between all cases or values and the measure of central tendency.
Dispersion and deviation are important to research. All variables have dispersion;
if not, they would not be variables (values that change between cases), they would be
Chapter 5
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constants (a constant value no matter what the case). Take juvenile delinquency, for
example. Some juveniles do not commit any delinquent acts during their teenage years
(at least theoretically), many juveniles commit s.
Research methodology
Experimental Studies
Concept of Variance
Partitioning of Variance
Control techniques
Sources of error variance
Commonly used Statistics in Medical Research Handout
We found this handout to be incredibly useful as a guide and resource for non-statistical professionals to make quick decisions about statistical methods. The handout accompanies the Commonly Used Statistics in Medical Research Part I Presentation
Advice On Statistical Analysis For Circulation Research
This document provides an overview and review of statistical methods for analyzing cardiovascular research data. It discusses common statistical errors in previous decades, such as low statistical power and inadequate analysis of repeated measures studies. It introduces several statistical methods that are useful but not always familiar to cardiologists, including power analysis, methods for analyzing repeated measures, analysis of covariance, multivariate analysis of variance, nonparametric tests, and more. The goal is to help researchers choose the appropriate statistical tests and properly interpret the results.
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...
Researchers should take several steps to make statistical results meaningful:
1. Perform a power analysis to determine adequate sample size and ensure power is above .50, ideally .80. Power is the probability of detecting real effects.
2. Never set the alpha level lower than .05 and try to set it higher to .10 if acceptable.
3. Report effect sizes and confidence intervals to provide context around statistical significance. Effect sizes indicate the magnitude of differences between groups.
Multiple Linear Regression II and ANOVA I
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.
stats notes.doc
This document provides an overview of key concepts in statistics including measures of central tendency, measures of dispersion, probability, correlation, time series analysis, and network planning methods like CPM and PERT. It defines terms like mean, median, mode, standard deviation, variance, probability, random experiment, correlation, time series, network, critical path, slack time, and differences between CPM and PERT. It also lists advantages and limitations of using PERT/CPM for project management.
Eviews forecasting
This document provides an overview of forecasting using Eviews 2.0 software. It distinguishes between ex post and ex ante forecasting. Ex post forecasts use known data to evaluate a forecasting model, while ex ante forecasts predict values using uncertain explanatory variables. The document then discusses univariate forecasting methods in Eviews, including trend extrapolation, modeling trend behavior, and analyzing residuals to check assumptions. It provides examples of estimating a trend model, viewing residuals, and making forecasts in Eviews.
Similar to Spss6 multiple regression (20)
Inferential AnalysisChapter 20NUR 6812Nursing Research
Inferential AnalysisChapter 20NUR 6812Nursing Research
Inferential AnalysisChapter 20NUR 6812Nursing Research
Inferential AnalysisChapter 20NUR 6812Nursing Research
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A researcher in attempting to run a regression model noticed a neg.docx
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Analytic Methods and Issues in CER from Observational Data
Chapter 12Choosing an Appropriate Statistical TestiStockph.docx
Chapter 12Choosing an Appropriate Statistical TestiStockph.docx
What do youwant to doHow manyvariablesWhat level.docx
What do youwant to doHow manyvariablesWhat level.docx
Commonly used Statistics in Medical Research Handout
Commonly used Statistics in Medical Research Handout
Advice On Statistical Analysis For Circulation Research
Advice On Statistical Analysis For Circulation Research
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...
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Spss6 multiple regression
- 1. MULTIPLE REGRESSION Dr. Vipul Patel
- 2. 2 Multiple regression is used to explore the relationship between one continuous dependent variable and a number of independent variables or predictors (usually continuous) Some of the main types of research questions that multiple regression can be used to address are: How well a set of variables is able to predict a particular outcome? Which variable in a set of variable is best predictor of an outcome? Whether a particular predictor variable is still able to predict an outcome when the effects of another variable is controlled for.
- 3. 3 The three types of multiple regression analysis are Standard or simultaneous Hierarchical or sequential stepwise
- 4. Standard Multiple Regression 4 This is the most commonly used multiple regression analysis. In this all independent (or predictor) variables are entered into the equation. This method tells you how much of the variance in your dependent variable can be explained by your independent variables. It also gives you an indication of the relative contribution of each independent variable.
- 5. Case: Standard Multiple Regression5 Research Questions: How well do the two measures of control (mastery, PCOISS) predict perceived stress? Which is the best predictor of perceived stress: Control of external events (Mastery scale) or control of Internal States (PCOISS)?
- 6. 6 Data requirement One continuous dependent variable (i.e., Total perceived stress) Two or more continuous independent variables (i.e, mastery, PCOISS).
- 7. Interpretation of Output 7 Multicollinearity Check that your independent variables show at least some relationship with your dependent variable (above 0.3 preferably). Also check that the correlation between each of your independent variable is not too high (above 0.9). In this case both of the scale (Total Mastery and Total PCOISS) correlates substantially with Total Perceived Stress (-0.611 and - 0.581). Look at the Collinearity Statistics, if the value of Tolerance is very low (near to 0), then we can say that multicollinearity is present. Tolerance below 0.1 indicates a serious problem and Tolerance below 0.2 indicates a potential problem (Menard, 1995). In this case, the value of tolerance for two independent variables is 0.722 in each case. If the largest VIF is larger than 10 then there is cause for concern (Myers, 1990).
- 8. 8 Outliers Scatterplot Mahalanobis distance Chi Square Table Normality Homoscedasticity Scatterplot
- 9. 9 Look at the Model Summary output table and check the R Square value. This value will tell you how much variance in the dependent variable is explained by independent variables. In this case, the value of R Square is 0.466 (i.e., 46.6%). This means that our two independent variables (i.e, Mastery and PCOISS) explain 46.8% variance in perceived stress.
- 10. 10 Look at the ANOVA output table. This will tell you the statistical significance of the model. The significance value (i.e., 0.000) is less than 0.05. it indicates that the model is statistically significant. We can conclude that our regression model predicts perceived stress significantly well.
- 11. 11 Next thing we want to know the relative contribution of each independent variables in the prediction of dependent variable. Look at the “Coefficients output table.” The standardize Beta Coefficient for Total Mastery and Total PCOISS are -0.422 and -0.358 respectively. For these values, check the significance value, too!!!
- 12. 12 Thank you!!! Dr. Vipul Patel vipulpat@gmail.com