Regression Analysis - Science method

Shaban Juma Ally, that is why one should use weighted least squares (WLS) regression. When the coefficient of heteroscedasticity is zero - which should not happen - then WLS regression becomes OLS regression.

Performing a linear regression in SPSS with three categorical independent variables (IVs) and one continuous IV involves several steps. Here’s a step-by-step guide:

For more detailed instructions and examples, you can refer to resources like this guide from UCLA or this tutorial from TidyStat.

Summing really is not a great approach unless the summed scores are scaled in a way that’s well known in application (and even then is problematic).

The mean has two advantages. 1) If the items have a fixed range interpretation is usually easier. If it’s a 1 to 7 scale then 1 is lowest, 7 highest and 4 in the middle. A summed scale is hard to interpret because of variation in number of items. 2) With missing items the sum treats missing as zero so it distorts the score. The mean treats them as if missing completely at random. This is not perfect but better than treating values as 0. Also with only a few missing items and problems are minor.

Ideally one would impute missing values but I’ve seen quite a few analyses that sum scores with missing data and end up with essentially garbage outcomes (if 0 is an impossible value it can really mess with results).

If there’s no missing data the analyses will be identical except for the interpretation issue. So generally the mean is the better and safer default.

- **Include Everyone**: Provides a broader, generalizable analysis but may weaken the relationship in regression due to the inclusion of the 'no' responses.

- **Section Out 'Yes' Cases**: Focuses on a specific subgroup, likely strengthening the relationship in regression but limiting generalizability.

There are other statistical tests and tools to develop a prognostic model for cancer using TCGA data. Firstly data should be recorded in a systematic manner which facilitates a easier analysis of prognostic model for cancer.

This comes from the depth of R. It means that the command anova() expects a different object type. Usually, it would simply be two model objects, like:

anova(modelnull, model1)

The object you pass to anova() is a vector of numbers. Looks like you have passed a vector of coefficients to anova, not a model object.

If none of your independent variables (IVs) correlate with the dependent variable (DV), it raises questions about the appropriateness of conducting a multivariable linear regression analysis. In linear regression, the independent variables are expected to have some level of correlation with the dependent variable to explain variation in the DV.

Yes, there are new developments in how econometrics combines economic factors and energy modeling

you can use the glmm.hp package in R. https://academic.oup.com/jpe/article/15/6/1302/6845730 https://academic.oup.com/jpe/article/16/6/rtad038/7444979

install.packages("glmm.hp")

library(glmm.hp)

library(MuMIn)

library(lme4)

mod1 <- lmer(Sepal.Length ~ Petal.Length + Petal.Width+(1|Species),data = iris)

r.squaredGLMM(mod1)

glmm.hp(mod1)

a <- glmm.hp(mod1)

plot(a)

When dealing with a large number of potential predictors and a limited number of observations, it's important to select variables carefully to avoid overfitting. The rule of thumb of having at least 10 observations per variable is a good guideline, but it's not a hard and fast rule. In your case, with 90 observations and about 20 variables, you should indeed consider reducing the number of predictors.

Both Boruta feature selection and stepwise AIC are valid approaches to variable selection, but they have their limitations. Here are a few suggestions to help you choose the best variables for your Poisson/negative binomial regression:

Kiran Tahir You need to evaluate the significance of the log odds using the coefficient's p-value, or you can also use the confidence interval to determine the significance of your estimates.

A positive log odds does not necessarily mean that the association is significant between the independent and dependent variables.

In order to assess the comparability of blood tubes and LIH tubes for clinical chemistry and immunoassay testing, this question explores the interpretation and consequences of statistical studies, such as Bland-Altman plots and regression analysis. Additionally, it is a graphical representation of the difference between two variables, such as the effectiveness of lithium heparinized plasma and serum in clinical chemistry and immunoassays. Through the clarification of statistical subtleties and the identification of noteworthy discoveries, scholars and researchers can enhance our comprehension of the fundamental mechanisms propelling distinctions—or absence thereof—between the two varieties of tubes. The scientific community, clinicians, and laboratory staff who choose tests and interpret results can all benefit from this research. Regression analysis and Bland-Altman plots, however, demonstrated that the majority of tests did not demonstrate any appreciable variations between serum and LIH. Nevertheless, the biological variation (BV) database's tolerance for error restrictions (TEa) was surpassed by a few analytes in this specific journal.

Yes of course, adjusting by age will remove the confounding factor of age. Actually, adjusting the model by a confounding factor is one way of two to remove its effect when checking the effect of another variable.

Look at this example:

if the equation of model with only cognitive score as x and the outcome as y is like this:

y = 1 + 5*x1

and equation of a model with only age:

y = 2 + 3*x2

Assuming that both variables have additive effect (which is may not be true)

then the final equation should be something like this:

2*y = 1 + 5*x1 + 2 + 3*x2 = 3 + 5*x1 + 3*x2

and it can be written like this: 2 * y/2 = (3 + 5*x1 + 3*x2)/2

y = 1.5 + 2.5* x1 + 1.5 * x2

And adding more and more variables to the model will definitely affect the coefficients

The other way is by stratification: you can just select homogeneous sub sample and fit a model and so on as I mentioned in the previous comment

There is another way "propensity score matching/ propensity weighted analysis" which is using the same model of the previous regression and adding weights to the patients which can be used in weighted analysis or scoring analysis ( but I don't encourage it in most cases it doesn't work unless you have a large sample )

This in general, but the question remains:

Is there results conclusive? Absolutely not, the only way that can eliminate the confounding factors is controlled randomized trials or a very big sample of the population like big clinical registries or census

In my opinion and from experience most studies group patients like this: ">18", "18-45", "46-65", "> 65"

In your case it deserves a good letter to the editor to criticize and obvious mistake and I would as the authors to send me their data to replicate their results.. there is a very big mistake if they did so.

>> Tooth loss and age are correlated variables and can't be included in the same model as they will produce a collinearity problem, it must do so.<<<

Hi Daniel Wright. Sure, I'm fine with just calling it an interaction. I'm just saying that if one wanted to use some other term, I prefer effect modification over moderation because it is neutral with respect to the nature of the interaction.

I have some questions.

1) Was there some treatment (or intervention) between the baseline and followup scores? If so, did all subjects receive it, or only some of them? And if so to that, how were they allocated to intervention vs control?

2) How many colleges are there? If the number is fairly large, it may be preferable to estimate a multilevel model with subjects at level 1 clustered within colleges at level 2.

You can use path analysis. Lavaan package in R will allow this and compute all relevant direct and indirect effects for you.

Decision trees are an ensemble of models. You can use the bagging methods such as random forest (i.e. perform models one by one and the accuracy will be an average of each model) or the boosted method (in this case the model will be performed based on the previous model weighting the errors made and correcting them ). However, the more these models become complex tuning their different parameters (e.g. deep in the tree, number of trees, how trees learn from previous model errors), the more it is difficult to interpret. Simple regressions are more used to understand how predictors affect your target variable and will support less multicolinearity between predictors implying the reduction of the number of predictors. Boosting models will be better to make predictions.

The right model depends on your research question and the bias-variance tradeoff i.e. the interaction between the complexity of your model, the accuracy of predictions, and the ability of the model to make predictions on new data.

If the SEM model specifies all the same "cause" and "effect" paths linking the (latent) variables as are implied by a regression/mediation model, then the regression results are pretty much redundant. The researcher might choose to include the regression results if such results are more likely to be familiar to, and understood by, the audience for the report than SEM would be.

Sometimes, SEM models only include linkages for the indicators of each latent variable separately, with those results being used to inform the construction of multiple-indicator scales for the theoretical variables. In that case the regression modeling is done directlyl on the (observed) scales, and hence the results do not correspond to anything in the SEM.

Hello Xiaoyi Shu

again, you did not answer why you want to split the sample. I can imagine that you want to adhere to the practice of cross-validation in the literature. This is this idea that when you change the model post-hoc and you do this in the "calibration sample" and a check in the "validation sample" brings the same results, then the post-hoc change is supported.

This idea is one of the many examples how predictive modeling and causal modeling (SEM, CFA) became intertwined during the decades. Cross-validation recently became very potent in the context of machine learning (=predictive modeling) where you apply very flexible functions that can fit the hell out of a feature space (i.e., the pattern of relationships among all variables). Thus, you can fit complex, nonlinear and interactive relationships. This flexibility comes at the price of overfitting (fitting the noise). In this scenario, cross-validation is very potent as the samples resulting from the split will not have exactly the permutations of all data points). Hence the overfitting will become visible and makes sense.

In the realm of SEM/CFA (but any factor model), relationships are linear and thus, not very prone to this kind of overfitting. The danger here is rather "fitting wrong structures" to the data (wrong parameters or factors). This will not change from sample to sample and hence, cross-validation will not provide evidence for the viability of your decisions. One can easily show by simulation that if you fit a wrongly specified model to the data (by tinkering) and you repeat the exercise in a splitted part of the sample, you will get the same seemingly supporting result.

Christian's and my note that you only eliminate valuable N by splitting does not need special references as it is the main implication of the role of N for the imprecision / uncertainty of any parameter estimation. Every introductory textbook on statistics will tell you that.

HTH

Holger

The primary goal of regression analysis is to identify the significant predictors of a dependent variable. I have a YouTube video on how to carry it out and to interpret it.

The p value for the overall F statistic indicates that the overall multiple correlation R (and R squared) value is not significantly different from zero at the .05 level (p is greater than .05). The reason for the non-significant result may be a small sample (as indicated by your degrees of freedom) and/or the presence of too many predictor variables. This also explains the large discrepancy between R squared and adjusted R squared. You are lacking statistical power to "detect" an effect.

Can you please show the output? And are you sure that you are talking about the standardized beta regression coefficient and not the unstandardized b coefficient? How many predictor variables?

And sample size shouldnt be an issue, since beta is just beta_x = b_x * sd(y)/sd(x).

Christian Geiser , you wrote that "After all, the researchers spent time and money collecting the data; they don't want others to benefit "for free.""

They have a publication, don't they? So they did earn their pay.

Often researchers are paid by the public, they work in public universities, they serve the public. Public money is spent in their institution, their salary, their instruments, their consumables, and their publications (many journals take money!). And after all, the data - the hard stuff that counts most - are kept secret. Even when the publication is in journals that require that the data are made available (as per their Instructions for Authors).

Of course, some human-related (typically medical patient) data may not be made fully available for data protection reasons, if the data would allow for an nearly unambiguous identification of individuals from the combination of subject-related data given (I think this is what you meant with possible IRB concerns). But this applies only for (some) clinical studies where a lot of variables are used or for the combination of extremely rare features.

In my opinion, publication includes publication of data, not just arbitrary summaries and conclusions drawn from it. When the data are not available, then it should not be regarded as a scientific publication. We (the scientific community) should set the bar as high as reasonably achievable, and today this means that the data should be available (ideally following the FAIR principles [https://en.wikipedia.org/wiki/FAIR_data]), either via the supplement or via some dedicated public database.

I have also seen papers where the authors claimed that the data are published because the individual data points were shown in scatter plots. This is not publishing data; the data shown in scatter plots is extremely hard to use, often data points are overlapping, and multivariate relationships can not be recovered at all.

I agree. Except when cleaning data and examining prior to running analysis, data on different scales are difficult to compare. My example is a real-world problem of two very different scales. For example, straight percentages and graphs that are not standardized/normalized can be tough to eye. So much so, I've seen many people get it wrong (including in my example).

There should be a causal effect of the independent variables on the dependent variable in regression analysis. Primary data gathered through questionnaire for the dependent variable would be influenced by the current happenings while the independent variables based on secondary data was influenced by past or historical happenings. Therefore, there would not true linkages between independent variables and the dependent variable. Therefore, running a regression with both Secondary and primary data in the same model would not give you best outcome.

Suppose you need to estimate m coefficients in a linear regression model. The sum of all real variables and the dummy variables you have entered (m-1 plus the free coefficient) cannot be greater than the number of your observations, since you will be solving a system of linear equations when estimating the coefficients.

Exact equality is also undesirable, because in this case (assuming linear independence of rows and columns) you will get a single solution. Thus you must have at least one more observation than m.

If this sum is greater than the number of your observations, it means that the amount of data does not allow you to build such a detailed model.

Hi Kevin!

This is not an answer, but I have the same doubts, I guess. If I understood your query correctly. When I add all my independent variables in the same analysis window for computing logistic regression with a categorical dependent variable, the significance of the beta coefficients for each variable differs from when I analyze them individually. In effect, I am getting differing predictors for my IV depending on whether I have clubbed the DVs or analyzed them separately. I am confused! If you found your answers, please help me understand what this means. Thank you! Kevin Glynn

Plz read my idea about it and send me your opinion about IEAC(R)

see https://www.researchgate.net/post/Is_the_linear_regression_the_best_fit_for_this_study

Not sure why you are re-asking this question.

I think, if THIS is unclear to you, you should take some statistics classes and consult a local statistician. If you don't know what to do after you got your results, I would presume that you also did not know what to do before the analysis. No offense!

ArcGIS has Geographically Weighted Regression (GWR) which can be used to regress a dependent variable over independent variables. It also takes into account spatial autocorrelation effects.

Can you be more specific please, and tell us something about your data and expectations?

Thanks, I will review

Ma'Mon Abu Hammad

It (relationship) refers to the degree and direction of association or dependence between them. It seeks to understand how changes in one variable are related to changes in another variable.

Correlation analysis is a statistical technique used to measure the strength and direction of the linear relationship between two continuous variables. It provides a numerical value, called the correlation coefficient, which ranges between -1 and +1. A correlation coefficient of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. Correlation coefficients closer to 1 or -1 indicate stronger associations, while coefficients closer to 0 indicate weaker associations.

Regression analysis, on the other hand, is a statistical technique that examines the relationship between a dependent variable and one or more independent variables. It allows for quantifying the impact of the independent variables on the dependent variable and estimating the regression coefficients. Regression analysis can determine not only the direction but also the magnitude and statistical significance of the relationship between the variables.

In simple linear regression, the relationship between two variables is modeled using a straight line. The slope of the line represents the change in the dependent variable associated with a unit change in the independent variable. The intercept term represents the expected value of the dependent variable when the independent variable is zero.

In multiple linear regression, the relationship is extended to include multiple independent variables. It allows for examining the individual effects of each independent variable while controlling for the effects of other variables.

Correlation does not imply causation. A strong correlation between two variables does not necessarily mean that one variable causes the other. Causal relationships require further investigation through experimental designs or other rigorous methods.

Good luck!!

What are "bmc" and "mvpa"?

Why would there be any linear dependency on age and height?

Chuck A Arize Removing is a bad idea, unless you are absolutely sure that those data points are bad measurements.

Nonlinear transformations are not a good idea, see why:

Jochen Wilhelm some instances use the word "hierarchical" when not all variables are entered together, but separetely or in blocks of variables. For the former one automatic algorithms may be used (but not recommended, as you know) like stepwise regression, whereas for the latter one typically the researcher decides which (blocks of) variables are entered in which order (blockwise regression).

As Bruce Weaver already mentioned, this is done very frequently in psychology, although it may be questioned if this is necessary, yet useful, or just a habit because everyone does it. In most psychological papers in such cases they are only interested in the delta R^2, for example to show that the increase in explained variance of an interaction term is significant (but miss that this could also be done by the squared semipartial correlation and no blockwise regression is needed).

I remember a paper (I believe about job satifaction or something similar) where they entered sociodemographic variables in a first block, typical predictors in a second block and new predictor variables in a third block to show that the typical ones explain more than socidemographic variables alone. The third block to show that the new predictors explain variance over and above the former ones. (In light of causality, I would cast some doubt about the results....)

But you are right, within each block and for the full model, the order of the variables do not have any meaning.

Does it help?

What is the meaning of categorical more than 2(ordinal)?

But still, If a variable is categorical and has more than two categories, You should use that variable as a dummy variable or indicator variable. Mahfooz Alam

There are a few options with ordinal outcomes but also treating the predictors (IV) as ordinal is trickier. As David L Morgan noted you can do this with some SEM software. You could also use ordinal logistic regression treating the predictors as continuous, dummy coding them or treating them as monotonic (the latter only available in the R brms package as far as I'm aware https://cran.r-project.org/web/packages/brms/vignettes/brms_monotonic.html ).

Its worth noting that these are all parametric models - its just that they don't assume a normal distribution of residuals in the model.

In your study, where you have measured the effects of physical, social, and cultural environments on student performance using ordinal scales, you can use ordinal regression analysis to answer your research questions.

To conduct the ordinal regression analysis, you do not necessarily need to compute a composite score for the questions. Instead, you can use each question as a separate predictor in the analysis. Each question represents a different aspect of the environment (physical, social, or cultural), and using them as separate predictors allow you to assess the unique contribution of each aspect to student performance.

Here's a general outline of the steps you can follow:

By using each question as a separate predictor in the ordinal regression analysis, you retain the specificity and granularity of the different aspects of the environment being studied. This approach allows you to explore the individual effects of physical, social, and cultural environments on student performance.

Keep in mind that ordinal regression assumes proportional odds, which means it assumes that the relationship between the predictors and the outcome is consistent across different levels of the outcome variable. It's important to assess this assumption, for example, by conducting tests of parallel lines.

Additionally, be cautious when interpreting the results as causal relationships. While ordinal regression can help identify associations between variables, establishing causal relationships requires rigorous experimental designs or the consideration of other potential confounding factors.

Overall, by using ordinal regression analysis and examining the effects of different environmental factors on student performance separately, you can address your research questions and gain insights into the influence of physical, social, and cultural environments on student performance.

If you want your regression model to predict integer values instead of decimal values, you can modify your approach by treating the problem as a classification task rather than regression. Instead of scaling the traffic volume between 0 and 1, you can map the integer values to a set of discrete classes. For example, you can define different classes such as 0-100, 101-200, 201-300, and so on, and assign each traffic volume to the corresponding class. Then, you can use a classification model like a neural network with softmax activation and categorical cross-entropy loss function to predict the class of each traffic volume. This way, your model will output integer predictions representing the class labels rather than decimal values.

"Significance" is not what should concern you. It is a function of sample size, and even if you compare x-variables with the same sample size in a multiple regression, issues such as collinearity could foul such comparisons. Of course if your sample size is too small, you won't be able to discover much of anything. But you might try plotting the points with a regression "line," and put curves around it using the estimated variance of the prediction error. Don't forget heteroscedasticity. I know SAS does a good job of this. You could put predicted-y on the x-axis and the y-values on the y-axis (or estimated residuals on the y-axis when looking for heteroscedasticity, which is natural, associated with the predicted-yi as a size measure).

Penn State has some good introductory material on this, though they did not include heteroscedasticity, the last time I looked. You can find information from Penn State by searching on a term, and including "Pennsylvania State University" in the search.

Best wishes.

Descriptive statistics is a vague term and usually applied to describing the properties of a single variable. However there is law that says that a correlation cannot be a descriptive statistic. We might make the distinction between descriptive and hypothesis testing statistics, for example.

I would imagine that a table of the intercorrelations of the items of a scale would be descriptive rather than hypothesis testing, for example.

But there's no legal definition, so no worries!

Hello again Md.,

I would recommend you try either path analysis (available in any SEM package) or the associated multiple linear regression models.

The SEM model would have these proposed relationships:

1. IV1 -> Med

2. IV2 -> Med

3. IV3 -> Med

4. Med -> DV

Good luck with your work.

Let's simplify things a bit and consider two models with X1 and X2 as the only explanatory variables, both quantitative.

1) Y = b₀ +b₁X₁ + b₂X₂ + error

2) Y = b₀ +b₁X₁ + b₂X₂ + b₃X₁X₂ + error

In model 1:

But those interpretations of b1 and b2 do not work for model 2. In model 2:

Putting it another way, b₁ and b₂ in model 2 are like simple main effects in a two-way ANOVA model, not like main effects in a two-way ANOVA model. Some authors describe them as "main effects", but I think that can cause confusion, and so I prefer to call them first order effects. HTH.

Hello Ibikunie,

1. Can an adjusted R-squared exceed 0.99? Yes.

2. Can an adjusted R-squared exceed the associated, unadjusted R-squared? No, though they can be equal (as pointed out by Debopam Ghosh )

Here's one version of the most commonly used formula for adjusted R-squared:

where:

R2 = unadjusted/observed R-squared

n = sample size used in model

k = number of IVs included in the model

Note that, the ratio (n - 1) / (n - k - 1) will always be less than one for k = 1, 2, ...n - 1. So, unless the unadjusted R-squared = 1, the adjusted R-squared will be less than the unadjusted R-squared. As N increases, relative to k, the difference between the two values will decrease as well.

Good luck with your work.

Extremely generic question: you must specify and detail.

Using multiple imputation or full information maximum likelihood (FIML) would probably be your best options. Under the assumption of missing at random (MAR) data, these techniques allow you to include all available data points in your analyses. Most other techniques either lead to a loss of data (and therefore statistical power), make more restrictive assumptions about the missing data mechanism, or both. See

Enders, C. K. (2022). Applied missing data analysis (2nd ed.). Guilford Press.

Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177. https://doi.org/10.1037/1082-989X.7.2.147

Carlos Araújo Queiroz I don't see a dataset, or am I missing something?

The Multinomial logistic regression is a statistical test that involves a single category variable which is predicted using one or more other factors. This method also establishes the numerical relation between such variable pairs. A categorical variable should be your targeted predictor. Linearity, independence, and the absence of outliers and multicollinearity are among the assumptions for multinomial logistic regression. For the details related to assumptions of multinomial logistic regression you may refer to following link:

A linear relationship, zero conditional mean of the error terms, Gaussian distribution of the error terms, homoskedasticity of the error terms, the absence of outliers, multicollinearity, and autocorrelation of the error terms are among the assumptions for linear regression. For more details you may use the following link:

Hope this would be useful.

R represents the correlation coefficient between two variables in a multivariable distribution. It measures the strength and direction of the linear relationship between the two variables. R ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

R^2, on the other hand, represents the coefficient of determination. It measures the proportion of variance in one variable that is predictable from the other variable(s) in a multivariable distribution. R^2 ranges from 0 to 1, where 0 indicates no variance in the dependent variable is explained by the independent variable(s), and 1 indicates that all the variance in the dependent variable is explained by the independent variable(s).

The main relationship between R and R^2 is that R is the square root of R^2. In other words, R^2 is the proportion of variance in the dependent variable that is explained by the independent variable(s), and R is the correlation coefficient between the dependent variable and the predicted values based on the independent variable(s). Therefore, R^2 is a measure of how well the regression line fits the data, while R is a measure of the strength and direction of the linear relationship between two variables. R-Squared? R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model

Have you compared thetwo univariate b's with their values in the full regression? Unstable estimates of these coefficients is the main problem in multicollinearity.

I suggest you try running the regression I suggested (two primary variables plus the multiplicative interaction effect) and see what happens.

It depends a little bit on the way your model will be designed and what are the available data.

In one of the most simplest ways you will have a mean energy consumption per human/animal/anything and you simply multiply by the number of individuals.

But i think that is not your intention.

Probably you have a data set with dfferent independent variables and you want one final response, that is not as simply associated as in my example above.

There are a couple of standard software tools available for a multiple (linear/non-liniear) regression. I would prefer R and the models of the lm type. Pretty good manuals are found around the web. But you may choose whatever you want; results should be the same.

An interesting introduction to the math behind is given in a paper by the US Geological Survey:

https://pubs.usgs.gov/tm/tm4a8/pdf/TM4-A8.pdf

However, depending on the specification of your problem it might be interesting to have a closer look at some other statistics.

When you can define specific groups (like high energy consumption time, low energy consumption time, medium, extraordinary, ...) a linear discriminant function analysis might be an interesting choice. It allows identifying specific variables, being characteristic (high contribution) for a predefined group.

A factor analysis might also be a good choice to identify higher/lower variable contributions.

If you are not really in charge to present the contributions of the variables a random Forest analysis might be interesting. This machine leraning classifyier can be also run as a regression model. You have less impression about the variables contributions, but the results can be more precise...

Nevertheless, it depends a bit on the available data. Did you already prepare a pairs plot and the correlation among the variables? This may also give a first impression....

Jan

Rede Ganeshkumar Dilipkumar so to answer the hypothesis test and relationship between regressor and regressand we need surely normality test right?... because oftenly in causal relationship method we have to prove if the hypothesis alternative is the answer or instead hypothesis null is the answer for answer the influence of regressor to regressand. So after we found the best fit model of regression whether pooled effect, fixed effect or random effect than we have to continue by finding the influence between regressor and regressand so you said that hypothesis test surely need normality test and other assumption test? .. Please put the recommended theory or reffrence to strengtening your argumentation. thank you for the enlightment..

Percent increase in explained variance (R square change) is not a very intuitive way to assess the practical significance of an interaction/moderation effect in my opinion. The percent increase could be small despite the fact that the interaction may be important. If the interaction is statistically significant, you should plot the regression lines for different meaningful values of the moderator to interpret the meaning and practical relevance of the interaction effect.

what is thadvantage of psm over ESR

What you are looking for is called linear regression. Good news is that linear regression is quickly done and easy to interpret. It will also give you more statistical power, as by categorization you loose information.

And don't worry, I've seen this categorization non-sense done by seasoned professors (and sometimes forced upon their students). That's from a past era, where you literally had to crunch the numbers with pencil and paper, which is easier with categories.

Hi,

In any regression result, there must be an ANOVA statistics. You have to check it in the Regression options given. In this wise, if that is the case, the a Multivariate Analysis is suitable and then you can run A regression Statistics afterwards. Your study has sub-variables if I understood you well, if you want to treat your dependent variable as just one whereas your independent variable has sub-variables, the you can find their combining effects..

In a situation where some companies do not have the ESG score, then you need to run a Student T-test statistics since they have a certain financial performance(Dependent Variable). You have to ascertain if there is a significant difference in the financial performances of comapnies that have the ESG score and those that do not have.

You can use factor analysis to group these items

"Would it be appropriate to execute linear regression analysis ... ?"

The answer depends on what you are trying to do, what you are trying to estimate and how much model-development you are prepared to do in the search for meaning and "optimal estimates".

In the present context what you could do is to do a simple linear estimation by least squares, but ignore the usual summary statistics that produce "error-bars" for estimates. Keep only only a single statistic. If you had only a single independent variable this could be just the regression coefficient. For multiple independent variables (as you later mention) you could use the reduction in the sum-of-squares from the regression. Then, to get a test for whether there is a real statistical association between your observed values, you could apply the principle of permutation testing whereby you evaluate the same summary statistic from exactly the same algorithm when applied to randomised versions of the original dataset. Here the randomisation provides a representation of the case of "no statistical association". The randomisation can be applied by doing a random permutation of the column of data for the dependent variable.

The principle here is that you can construct any measure of association you like and obtain a valid statistical inference by a first-principles argument involving randomisation. You mention "multiple cities". Notionally, it is just a matter of constructing an overall measure of association to summarize across all cities and then doing the randomisation separately for each city (but within the same step).

Note that the above centres on the question "to see if there is a correlation between these two variable". If you really want some sort of predictive model, or are extremely concerned about extracting as much information as possible from the data, then you would need to develop a full statistical model and this would take you well away from a simple least squares analysis.

Good morning. I understand fully as I've been doing independent work also. http://sites.google.com/site/deborahhilton/ Most of my work is on research gate though. I just try to work out the statistics myself also with textbooks I have here. If you had some specific questions I maybe able to answer for a nominal fee if you were wanting some reference material. Good luck. T-you.

It is a measure of goodness of fit in logistic regression analysis. It is a modification of the Cox and Snell R Square, which is derived from the likelihood ratio test statistic.

Nagelkerke R Square ranges from 0 to 1, with values closer to 1 indicating a better fit of the model. However, unlike in linear regression analysis, where R Square can be interpreted as the proportion of variance explained by the model, Nagelkerke R Square cannot be interpreted as easily.

A common rule of thumb is to interpret it, a value of 0.2 or less indicates a weak relationship between the predictors and the outcome.

A value of 0.2 to 0.4 indicates a moderate relationship.

A value of 0.4 or higher indicates a strong relationship.

However, it's important to note that the interpretation of Nagelkerke R Square should be taken with caution and should be supplemented by other measures of model fit, such as the Hosmer-Lemeshow test, AIC, or BIC. Additionally, it's essential to consider the practical significance of the relationship between the predictors and the outcome, rather than solely relying on statistical significance or goodness of fit measures.

It could be a power problem. When your samples get smaller, you reduce the statistical power to detect an effect. A better way to do this would be to include gender as a binary predictor into the overall analysis (and also potentially the interaction/product term housing*gender). That way, you can examine a potential gender (and interaction) effect without splitting your sample or running separate analyses.

Also, I would examine the data graphically using histograms, scatterplots etc. to see whether there are any peculiarities in the scores and their distributions (e.g., outliers, non-linear effects, etc.).

What the model requires is that the errors are mutually independent and identically distributed in a way that is approximating a Normal distribution with mean equal to 0 and variance equal to σ ².

Also, I remind you that linear regression is a mathematical function based on the equation of the geometric straight line.

The rest comes by itself.

Is this a nested sampling design where the students and/or parents from the second sample are nested within the workers and/or leaders? If that is the case, then perhaps multilevel (hierarchical linear) regression modeling could be an option. However, this requires nesting of observations, e.g., that the parents in Sample 2 can be linked to workers/leaders in Sample 1.

If the data aren't nested but there's some other connection/dependency between the observations in both samples, perhaps you could account for missing data by using full information maximum likelihood estimation or multiple imputation so that you wouldn't waste any data. But again, this requires that at least some observations can be linked across the two samples.

Yes, it can.

It is good that you carefully review the data matrix.

Also, try to understand carefully which are the dependent and possibly independent variables that you are interested in analyzing.

You haven't said what your research question(s) is(are), or what your goal of reducing the dimensionality of these 20 items is. It doesn't make sense to me (obviously it does to others ... see above!) to try to answer your question without this information (and again, those above obviously don't think these are important questions).