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# What does a low adjusted r squared mean

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1. In regression analysis, you'd like your regression model to have significant variables and to produce a high R-squared value. This low P value / high R 2 combination indicates that changes in the predictors are related to changes in the response variable and that your model explains a lot of the response variability.. This combination seems to go together naturally
2. R-squared and Adjusted R-squared are two such evaluation metrics that might seem confusing to any data science aspirant initially. Since they both are extremely important to evaluate regression problems, we are going to understand and compare them in-depth
3. How to Interpret a Regression Model with Low R-squared and Low P values Published on November 29, 2016 November 29, 2016 • 10 Likes • 1 Comment
4. If anyone can mention me in any journal article or book about low R-squared and adjusted R-square values, it will be highly appreciated. Regression Analysis. Share . Facebook. Twitter
5. Conversely, a low R squared means Y is poorly predicted by the covariates. Of course, an effect can be substantively important but not necessarily explain a large amount of variance Adjusted R squared. So, the simple R squared estimators is upwardly biased
6. low R-squared! Social Research Network 3nd Meeting Noosa April 12-13, 2012 model and the total sum of squares around the mean. Interpreted as the ration of variance explained by a regression model zAdjuseted R-squared= factor the size of R squared does not matterfactor, the size of R squared does not matter
7. Agreed. A low R-squared means the model is useless for prediction. If that is the point of the model, it's no good. I don't know anything specifically about hypertension studies and typical R-square values. Anyone else want to comment? And it's a good point that most studies don't mention assumption testing, which is too bad

### How to Interpret a Regression Model with Low R-squared and

R-squared does not indicate if a regression model provides an adequate fit to your data. A good model can have a low R 2 value. On the other hand, a biased model can have a high R 2 value! Are Low R-squared Values Always a Problem? No! Regression models with low R-squared values can be perfectly good models for several reasons The adjusted R-squared in Regression 1 was 0.9493 compared to the adjusted R-squared in Regression 2 of 0.9493. Therefore, the adjusted R-squared is able to identify that the input variable of temperature is not helpful in explaining the output variable (the price of a pizza) Adjusted r-square is a ratio on a scale from zero to one. Researchers use the adjusted r-square to test the strength of the model. It is also an indicator of which variables to include in a data model. If the researcher removes one variable and the adjusted r-square increases, the researcher knows there is a problem with that variable A fund with a low R-squared, at 70% or less, indicates the security does not generally follow the movements of the index. A higher R-squared value will indicate a more useful beta figure

Adjusted ${R^2}$ also indicates how well terms fit a curve or line, but adjusts for the number of terms in a model. If you add more and more useless variables to a model, adjusted r-squared will decrease. If you add more useful variables, adjusted r-squared will increase. Adjusted ${R_{adj}^2}$ will always be less than or equal to ${R^2}$ Adjusted R Squared or Modified R^2 determines the extent of the variance of the dependent variable, which can be explained by the independent variable. The specialty of the modified R^2 is it does not take into count the impact of all independent variables rather only those which impact the variation of the dependent variable A low r-squared figure is generally a bad sign for predictive models. However, in some cases, a good model may show a small value. There is no universal rule on how to incorporate the statistical measure in assessing a model. The context of the experiment or forecast Forecasting Methods Top Forecasting Methods In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced R squared, is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).. It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related. If you want a portfolio that doesn't move at all like the benchmark, you'd want a low R-squared. An R-squared measure of 35, for example, means that only 35% of the portfolio's movements can be.

### Difference Between R-Squared and Adjusted R-Squared

• The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or: R-squared = Explained variation / Total variation. R-squared is always between 0 and 100%: 0% indicates that the model explains none of the variability of the response data around its mean
• Negative R-squared is often encountered when you test a model (that has high bias and/or high variance) using out of sample data. An example of a high bias model is a linear regression model with non-stationary residuals (i.e., a spurious regressi..
• Just because a model a has a low R-Squared does not mean it is a bad model. R-Squared is often said to measure the goodness of fit of a regression line however this can be misleading
• No I meant p < 0.05 means at least one of your means is different. A low R squared implies a low R implies a weak fit and causes you to have a low confidence in the value of p. Jim Shelor. 0. August 28, 2007 at 5:03 pm #160498
• For instance, low R-squared values are R-squared does not we'll continue with the theme that R-squared by itself is incomplete and look at two other types of R-squared: adjusted R.
• ed by the benchmark index, perhaps by containing securities only from that index. A low R.
• If you have a very low r^2, then it is reasonably easy to get negative values. Granted, a negative adjusted r^2 does not have any more intuitive meaning than regular r^2, but as the previous commenter says, it just means your model is very poor, if not just plain useless
• ation, variance explained, the squared correlation, r 2, and R 2. We get quite a few questions about its interpretation from users of Q and Displayr , so I am taking the opportunity to answer the most common questions as a series of tips for using R 2
• R-Squared only works as intended in a simple linear regression model with one explanatory variable. With a multiple regression made up of several independent variables, the R-Squared must be adjusted. The adjusted R-squared compares the descriptive power of regression models that include diverse numbers of predictors
• So, Adjusted R-square can decrease when variables are added to a regression. Hence, adjusted R² will only increase when the added variable is relevant. Note that Adjusted R² is always less than.

The value of Adjusted R Squared decreases as k increases also while considering R Squared acting a penalization factor for a bad variable and rewarding factor for a good or significant variable. Adjusted R Squared is thus a better model evaluator and can correlate the variables more efficiently than R Squared The adjusted R-squared plateaus when insignificant terms are added to the model, and the predicted R-squared will decrease when there are too many insignificant terms. A rule of thumb is that the adjusted and predicted R-squared values should be within 0.2 of each other. There is no commonly used cut-off value for R-squareds. Analysis.

### How to justify low R-squared and adjusted R-square value

R-squared does not indicate if a regression model provides an adequate fit to your data. A good model can have a low R 2 value. On the other hand, a biased model can have a high R 2 value! Are Low R-squared Values Always a Problem? No. Regression models with low R-squared values can be perfectly good models for several reasons 2 thoughts on What Is R Squared And Negative R Squared ali February 8, 2018 at 10:10 am. Hi, Thanks for this very simple and informative post! I am trying to model a stock market time series data via LSTM. I have observed that my RMSEs on both train and test sets are almost identical in addition to a positive correlation between the predictions and the original values in the test set Concerning R2, there is an adjusted version, called Adjusted R-squared, which adjusts the R2 for having too many variables in the model. Additionally, there are four other important metrics - AIC , AICc , BIC and Mallows Cp - that are commonly used for model evaluation and selection Alpha, a risk-adjusted performance measure, also is unlikely to provide a usable figure if the security or portfolio has a low R-squared rating. This is because the underlying benchmark used in the beta and alpha calculations does not have significant relevance to the stock or portfolio's movement to begin with depends, R squared is a measure of noise, how well your line fits the data. a low value means that the values vary quite a lot from the regression line/prediction. a high R squared means that the points all lie close to the regression line. The.

From the above, we can observe that both the r-squared and adjusted r-squared are reasonably high, however only one of the coefficient values has a significant p-value, C3. Note: Maple shows all p-values less than 0.05 in bold. Let's try to fit the data again, this time keeping the two coefficients with the lowest p-values and the intercept Difference Between R-Squared and Adjusted R-Squared. While building regression algorithms, the common question which comes to our mind is how to evaluate regression models.Even though we are having various statistics to quantify the regression models performance, the straight forward methods are R-Squared and Adjusted R-Squared For an example of a pseudo R-squared that does not range from 0-1, consider Cox & Snell's pseudo R-squared. As pointed out in the table above, if a full model predicts an outcome perfectly and has a likelihood of 1, Cox & Snell's pseudo R-squared is then 1- L(M Intercept ) 2/N , which is less than one Hi all. I'm fairly new to predictive modeling, and I'm working on generating a model in SPSS Statistics. I have about 8 variables that are significant, and when I run the validation, I get an adjusted R squared of about 0.4. I don't know how to interpret this. Does this mean it has an accuracy level of 40%? Does that mean it's a good model

Adjusted R Squared : A measure of how well the independent, or predictor, variables predict the dependent, or outcome, variable. A higher adjusted R-square indicates a better model Definition: R squared, also called coefficient of determination, is a statistical calculation that measures the degree of interrelation and dependence between two variables.In other words, it is a formula that determines how much a variable's behavior can explain the behavior of another variable. What Does R Squared Mean Reason 1: R-squared is a biased estimate. The R-squared in your regression output is a biased estimate based on your sample—it tends to be too high. This bias is a reason why some practitioners don't use R-squared at all but use adjusted R-squared instead. R-squared is like a broken bathroom scale that tends to read too high. No one wants that

R squared and adjusted R squared for panel models. This function computes R squared or adjusted R squared for plm objects. It allows to define on which transformation of the data the (adjusted) R squared is to be computed and which method for calculation is used So an R-squared of 0.65 might mean that the model explains about 65% of the variation in our dependent the point being made is that R-squared does not measure goodness of fit. Shalizi gives even more reasons in his lecture notes. And it should be noted that Adjusted R-squared does nothing to address any of these issues

Adjusted R 2 is a corrected goodness-of-fit (model accuracy) measure for linear models. It identifies the percentage of variance in the target field that is explained by the input or inputs. R 2 tends to optimistically estimate the fit of the linear regression. It always increases as the number of effects are included in the model Difference between R-square and Adjusted R-square. Every time you add a independent variable to a model, the R-squared increases, even if the independent variable is insignificant.It never declines. Whereas Adjusted R-squared increases only when independent variable is significant and affects dependent variable.; In the table below, adjusted r-squared is maximum when we included two variables

### R squared and adjusted R squared - The Stats Gee

adjusted R-square = 1 - SSE(n-1)/SST(v) The adjusted R-square statistic can take on any value less than or equal to 1, with a value closer to 1 indicating a better fit. Negative values can occur when the model contains terms that do not help to predict the response. Root Mean Squared Erro If the R 2 statistic is ignored here, a team may veer off track and not find other critical Xs. Notice that the total adjusted R 2 = 32.6 percent. Since only 32.6 percent of the variation is explained by X 1 and X 2, that means that 67.4 percent of the variation is unaccounted for

R-Squared or Coefficient of Determination If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked Can a Regression Model with a Small R-squared Be Useful? http://www.theanalysisfactor.com/small-r-squared/[12/16/2013 9:50:46 AM] collected on every possible control 4. R Squared. It is also known as the coefficient of determination.This metric gives an indication of how good a model fits a given dataset. It indicates how close the regression line (i.e the predicted values plotted) is to the actual data values. The R squared value lies between 0 and 1 where 0 indicates that this model doesn't fit the given data and 1 indicates that the model fits perfectly. In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and -1. To interpret its value, see which of the following values your correlation r is closest to: Exactly -1. A perfect downhill (negative) linear relationship [

### Video: Can a Regression Model with a Small R-squared Be Useful

What does it mean and how do we calculate it?. Partial R 2 simply means how much of the Corrected Total Sums of Squares can we attribute to the Sums of Squares for this particular effect. So, if we have an Effect (line in our ANOVA table), for example, a regression term b 3 , the its partial R 2 would be SSb 3 /(CTSS) In SPSS, exactly what do R, R-squared and F mean in the output of a Linear Regression ? What would a low and a high value indicate for a relationship between two variables? Quote from a given assignment: ''Report and interpret (in plain English, so as to make clear that you understand what it means) R, R2, the F-test on the model, the regression coefficients (Constant and B)

If all assumptions of the models are verified, yes The R-squared value is the amount of variance explained by your model. It is a measure of how well your model fits your data. As a matter of fact, the higher it is, the better is your model. However, it only applies when te assumptions of the models are fulfilled (e.g. for a linear regression : homogeneity and normality of the data. Analysis: If R Squared is greater than 0.80, as it is in this case, there is a good fit to the data. Some statistics references recommend using the Adjusted R Squared value. In this example, R Squared of 0.980 means that 98% of the variation can be explained by the independent variables

### R-Squared vs. Adjusted R-Squared: What's the Difference

Key properties of R-squared. R-squared, otherwise known as R² typically has a value in the range of 0 through to 1.A value of 1 indicates that predictions are identical to the observed values; it is not possible to have a value of R² of more than 1. A value of 0 indicates that there is no linear relationship between the observed and predicted values, where linear in this context means. R-squared is a measure of how well a linear regression model fits the data.. It can be interpreted as the proportion of variance of the outcome Y explained by the linear regression model. It is a number between 0 and 1 (0 ≤ R 2 ≤ 1). The closer its value is to 1, the more variability the model explains In the example below, we can see the graph on the left has no relationship, as indicated by low R-squared value. The graph on the right has a very strong relationship, as indicating by the R-squared value of 1. In none of these graphs can we tell what is ultimately causing this relationship. Correlation does not mean causation

Q&A about R 2 What does R 2 quantify • The value R 2 quantifies goodness of fit. It compares the fit of your model to the fit of a horizontal line through the mean of all Y values. • You can think of R 2 as the fraction of the total variance of Y that is explained by the model (equation). With experimental data (and a sensible model) you will always obtain results between 0.0 and 1.0 R-squared value synonyms, R-squared value pronunciation, Our general finding is that the predictive ability of these models is relatively low as the highest within R-squared value is 0.2439 and the lowest is 0.0315. with the adjusted R-squared value of 0.1337

R 2 and adjusted R 2 are often used to assess the fit of OLS regression models. Below we show how to estimate the R 2 and adjusted R 2 using the user-written command mibeta, as well as how to program these calculations yourself in Stata.Note that mibeta uses the mi estimate command, which was introduced in Stata 11. The code to calculate the MI estimates of the R 2 and adjusted R 2 can be used. The adjusted sum of squares does not depend on the order the factors are entered into the model. They are obtained by setting each calculated mean square equal to its expected mean square, which gives a system of linear equations in the unknown variance components that is then solved R-squared vs. adjusted R-squared Two common measures of how well a model fits to data are $$R^2$$ (the coefficient of determination) and the adjusted $$R^2$$. The former measures the percentage of the variability in the response variable that is explained by the model Correlation (otherwise known as R) is a number between 1 and -1 where a v alue of +1 implies that an increase in x results in some increase in y, -1 implies that an increase in x results in a decrease in y, and 0 means that there isn't any relationship between x and y This means that the likelihood value for each observation is close to The low R squared for the individual binary data model reflects the fact that the covariate x does not enable accurate prediction of the individual binary In linear regression, the standard R^2 cannot be negative. The adjusted R^2 can however be negative

Modified r-squareds are offered to overcome the deficiencies of the usual and adjusted r-squareds in linear models with trending and seasonal data.These modified measures are shown to be consistent for the population r-squared when the data contain deterministic trends in the mean, or deterministic seasonal components in the mean, or both Adjusted R squared The adjusted R squared is obtained by using the adjusted sample variances and instead of the unadjusted sample variances and . This is done because and are unbiased estimators of and under certain assumptions (see the lectures entitled Variance estimation and The Normal Linear Regression Model ) If the r-squared value is high, it indicates how useful its beta figure is. If a fund with r-squared value is 100 or in a higher range but has a beta which is below 1 then it is offering a high risk-adjusted return, and low r-squared value would not have any standing in the market, so it is best to ignore the beta of the low r-squared fund

### How to Interpret Adjusted R-Squared and Predicted R

R-squared is a statistical measure that represents the goodness of fit of a regression model. The ideal value for r-square is 1. The closer the value of r-square to 1, the better is the model fitted. R-square is a comparison of residual sum of squares (SS res) with total sum of squares(SS tot).Total sum of squares is calculated by summation of squares of perpendicular distance between data. Least square means are means for groups that are adjusted for means of other factors in the model. Imagine a case where you are measuring the height of 7th-grade students in two classrooms, and want to see if there is a difference between the two classrooms R-squared and Adjusted R-squared: The R-squared value means that 61% of the variation in the logit of proportion of pollen removed can be explained by the regression on log duration and the group indicator variable. As R-squared values increase as we ass more variables to the model, the adjusted R-squared is often used to summarize the fit a

I have a question concerning the difference between the linkage disequilibrium measures D' and r-squared. I know the formal definitions. But I have problems understanding the different concepts behind D' and r-squared? And what does it mean if D' is low and r-squared is high (and vice versa). Thanks wi R squared does have value, but like many other measurements, it's essentially useless in a vacuum. Some examples: it can be used to determine if a transformation on a regressor improves the model fit. adjusted R 2 can be used to compare model fit with different subsets of regressors. a low R 2 and low p-values can indicate multicollinearit R-Squared (within, between, overall) 24 Oct 2015, 11:16. Dear stata users, I am building a model to predict firm return volatility, if historical returns are not available. My model is based on firm characteristics like size, industry, d/e ratio, etc.. I want. Multiple R-squared: 0.5009, Adjusted R-squared: 0.4296 F-statistic: 7.026 on 2 and 14 DF, p-value: 0.00771 ### p-value and (multiple) R-squared value. Simple plot of data and model. For bivariate data, the function plotPredy will plot the data and the predicted line for the model A fund has a sample R-squared value close to 0.5 and it is most likely offering higher risk-adjusted returns with the sample size of 50 for 5 predictors. Given, Sample size = 50 Number of predictors = 5 Sample R -square = 0.5 . To Find, Adjusted R square value. Solution: Substitute the values in the formula

If the R squared is very low, meaning that X isn't connected to Y, it's a sign that using X to predict Y simply isn't buying you much; you might as well use the mean of Y for every guess. Unlike significance tests, there aren't thresholds for R squared to tell you if your value is 'good enough' The first model yields an R 2 of more than 50%. The second model adds cooling rate to the model. Adjusted R 2 increases, which indicates that cooling rate improves the model. The third model, which adds cooking temperature, increases the R 2 but not the adjusted R 2.These results indicate that cooking temperature does not improve the model It is here, the adjusted R-Squared value comes to help. Adj R-Squared penalizes total value for the number of terms (read predictors) in your model. Therefore when comparing nested models, it is a good practice to look at adj-R-squared value over R-squared.  R^{2}_{adj} = 1 - \frac{MSE}{MST}\$ Concept of R-squared, Example calculating R-squared Why are there 2 types of R-squared? Example calculating adjusted R-squared Adjusted R Squared = 1 - (((1 - 64.11%) * (10-1)) / (10 - 3 - 1)) Adjusted R Squared = 46.16%; Explanation. R 2 or Coefficient of determination, as explained above is the square of the correlation between 2 data sets. If R 2 is 0, it means that there is no correlation and independent variable cannot predict the value of the dependent variable. . Similarly, if its value is 1, it means.

If the model is so bad, you can actually end up with a negative R-Squared. Adjusted R-Squared. Multiple R-Squared works great for simple linear (one variable) regression. However, in most cases, the model has multiple variables. The more variables you add, the more variance you're going to explain Nagelkerke's R 2 2 is an adjusted version of the Cox & Snell R-square that adjusts the scale of the statistic to cover the full range from 0 to 1. McFadden's R 2 3 is another version, based on the log-likelihood kernels for the intercept-only model and the full estimated model The R-squared and adjusted R-squared values are 0.508 and 0.487, respectively. Model explains about 50% of the variability in the response variable. Access the R-squared and adjusted R-squared values using the property of the fitted LinearModel object

### What does it mean to have a low R-squared ? A warning

R-squared ranges from 0 to 100 and reflects the percentage of a fund's movements that are explained by movements in its benchmark index. An R-squared of 100 means that all movements of a fund are. The coefficient of determination (R 2) and t-statistics have been the subjects of two of my posts in recent days (here and here).There's another related result that a lot of students don't seem to get taught. This one is to do with the behaviour of the adjusted R 2 when variables are added to or deleted from an OLS regression model. We all know, and it's trivial to prove, that the addition. R-squared, or R2, in mutual funds, is a statistical benchmark that investors can use to compare a fund to a given benchmark. R-squared values are expressed as a percentage between 1 and 100. A higher R-squared value means the fund moves with the benchmark Question: R Squared, Adjusted R Squared P-what Does It Mean T- What Does It Mean, Rule Of Thumb, How To Calculate. This problem has been solved! See the answer. Show transcribed image text. Expert Answer . Previous question Next question Transcribed Image Text from this Question R-squared is commonly used to summarize a statistical relationship or statistical correlation between two events. While that may be true, it does not prove that there is a causal relationship. As with most statistical models, their predictive power is only as good as the understanding of the events themselves

### Low R-squared values in multiple regression analysis

r-squared is really the correlation coefficient squared. The formula for r-squared is, (1/(n-1)∑(x-μx) (y-μy)/σxσy) 2. So in order to solve for the r-squared value, we need to calculate the mean and standard deviation of the x values and the y values. We're now going to go through all the steps for solving for the r square value Despite the fact that adjusted R-squared is a unitless statistic, there is no absolute standard for what is a good value. A regression model fitted to non-stationary time series data can have an adjusted R-squared of 99% and yet be inferior to a simple random walk model Though a little more esoteric, R-Squared is similar to Beta, but in this case tells you what proportion of a stock's risk is market-related, a figure that cannot be adjusted by diversification the way beta can. A completely diversified portfolio would be perfectly correlated to the market, indicative of an R-Squared figure of 1.0 Alternatively, your R-squared may be low, but no indictment of your model, if the field is refractory and your dataset is problematic. As R -squared never decreases as you add covariates (predictors), a high R -squared may go with a model that on scientific or statistical grounds has too many covariates

### How To Interpret R-squared in Regression Analysis

Index funds will have an R-squared very close to 100. On the other end, a low R-squared means much lower amount of a portfolio's movements can be explained by movements in its benchmark index. An R-squared measure of 30 means that only 30% of the portfolio's movements are aligned to the benchmark index movements. Got it? R-Squared in Mutual. It is worth emphasizing that a seemingly low r - squared does not necessarily mean that an ols regression equation is useless 在社會科學中，特別是在截面數據分析中,回歸方程得到低的r -平方值并不罕見� Definition of Adjusted R Squared in the Titi Tudorancea Encyclopedia. Meaning of Adjusted R Squared. What does Adjusted R Squared mean? Proper usage and sense of the word/phrase Adjusted R Squared. Information about Adjusted R Squared in the Titi Tudorancea encyclopedia: no-nonsense, concise definitions Linear mixed effects models are a powerful technique for the analysis of ecological data, especially in the presence of nested or hierarchical variables. But unlike their purely fixed-effects cousins, they lack an obvious criterion to assess model fit. [Updated October 13, 2015: Development of the R function has moved to my piecewiseSEM package, which can b

### Adjusted R-squared - Overview, How It Works, Exampl

The Adjusted R Squared is such a metric that can domesticate the limitations of R Squared to a great extent and that remains as a prime reason for being the pet of data scientists across the globe. Although it is not in the scope of this article, please have a look at some other performance evaluation metrics which we usually use in regression and forecasting here like MAE, MSE, RMSE, MAPE, etc Now the other number, Root Mean Squared Error, I've calculated it for the three examples here. And it's 32, 4 and 32, somewhat coincidentally for the production time dataset. Now, one key difference between R squared and RMSE are the units of measurement. So R squared, because it's a proportion, actually has no units associated with it at all

R-squared provides the relative measure of the percentage of the dependent variable variance that the model explains. R-squared can range from 0 to 100%. An analogy makes the difference very clear. Suppose we're talking about how fast a car is traveling. Example Regression Model: BMI and Body Fat Percentag However, this does not appear in the final comparison table. It does work however, when I run the fixed effects models instead of random effects models. I would like to understand why the R-squared statistic is not displayed in the regression comparison table and how I can fix this Mean square error; We illustrate these concepts using scikit-learn. So if it is 100%, the two variables are perfectly correlated, i.e., with no variance at all. A low value would show a low level of correlation, meaning a regression model that is not valid, but not in all cases. Reading the code below,. So, how does the adjusted and regular R-squared differ? 1. Adjusted R-squared value takes into account the number of I NDEPENDENT variables in the model, whereas the regular R-squared does not. 2. In fact, if we add new independent variables to our mode l, the adj usted R-sq uared va lue wil EC Analaytics - Learn Power BI, Excel VBA, Python Data. > R-squared value. I was surprised to see that the R-squared value I obtained > from SAS was different. So I went back to Excel, did Regression under Tools > > Data Analysis, set the intercept to 0 also, and the R-squared value was the > same as the value I obtained from SAS. > > I thought that maybe there was something wrong with my data, so.

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