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# Y bar vs y hat

### statistics - How to show for a simple regression with an

• $\begingroup$ so , the difference between y hat and y bar is that y hat is a value on the regression line and y bar is just a mean number? $\endgroup$ - user1919987 Oct 30 '14 at 6:27 $\begingroup$ @user1919987 yes, you are correct, hope this was helpful, good thinking. $\endgroup$ - drphil Oct 30 '14 at 14:5
• Predicted Value Y-hat. Y-hat ( ) is the symbol that represents the predicted equation for a line of best fit in linear regression. The equation takes the form where b is the slope and a is the y-intercept. It is used to differentiate between the predicted (or fitted) data and the observed data y
• utes!
• d: y-hat (ŷ) is the predicted value of y. Y-bar (ȳ) is the mean of the response, and y is the actual response value. The psu.edu link at the end of this section does a great job of going into detail about below and I borrow liberally from them. I recommend looking at the examples there for more information
• E1 = predict values of Y based on Y bar (mean) sum of (Y - Y bar) 2; E 2: predict Y based on X and regression line sum of (Y - Y hat) 2 (deviation of observed Y from regression line, squared) Correlation: r Pearson correlation coefficient or product-moment coefficien

Y bar is how you read the symbol $\bar{y}$. In statistics, the variable $y$ is conventionally used for observations of something you want to predict. There's no logic for that, it's just convention. For example, if you were.. Y is for Ys, Y-hats, and Residuals. When working with a prediction model, like a linear regression, there are a few Ys you need to concern yourself with: the ys (observed outcome variable), the y-hats (predicted outcome variables based on the equation), and the residuals (y minus y-hat). Today, I'll dig into the different flavors of y and how. The first chart has std residuals on the X axis and fitted values of Sales Price on Y. The 2nd chart is has std residuals vs just the y value (Sales Price). Multiple regression model predicting real estate Sales Price with IV's: Age, Living Area, and Garage. Last edited: Jun 3, 2015 The sample average of y-variable. That we already calculated and saved it in a variable 'y_bar'. For assessing, how well the regression model fits the dataset, all these y_i, y_ihat and y_bar will be very important. The distance between y_ihat and y_bar is called the regression component. regression component = y_ihat — y_bar

σ p̂ sigma-sub-p-hat; see SEP above. ∑ sigma = summation. (This is upper-case sigma. Lower-case sigma, σ, means standard deviation of a population; see the table near the start of this page.) See ∑ Means Add 'em Up in Chapter 1. χ² chi-squared = distribution for multinomial experiments and contingency tables Thanks for contributing an answer to Cross Validated! Please be sure to answer the question.Provide details and share your research! But avoid . Asking for help, clarification, or responding to other answers The points on the regression line corresponding to the original x values are: y-hat (1)=1.4, y-hat (2)=2.7, y-hat (4)=5.3, y-hat (5)=6.6. The regression line can also be used to provide the best estimate for the y value associated with an x value which is not given: y-hat (3)=4. The least squares regression line is displayed in the following.

### What is the difference between Y and Y hat

1. Y-hat is the symbol that represents the predicted equation for a line of best fit in linear regression.The equation takes the form where b is the slope and a is the y-intercept.It is used to differentiate between the predicted (or fitted) data and the observed data y.Y-hat is also used in calculating the residuals of , which are the vertical differences between the observed and fitted values
2. The Residuals vs Fitted plot shows the residuals versus the fitted values $$\hat{y_i}$$. It might seem more natural to plot residuals against the explanatory variables $$x_i$$, and in fact for simple linear regression it does make sense to do that
3. If a variable y is linearly related to x, then we use the formula for a line: ^ y = mx + b. Or more commonly in the context of regression, ^ y = b 0 + b 1 x where b 1 is the slope of the line, and b 0 is the y-intercept. Note that the y has a caret (^) over it. This is pronounced y-hat and means it is our estimated value of y
4. ology: The mean of the random variable Y is also called the expected value or the expectation of Y. It is denoted E(Y). It is also called the population mean, often denoted µ.It is what we do not know in this example.; A sample mean is typically denoted ȳ (read y-bar). It is calculated from a sample y 1, y 2, , y n of values of Y by the familiar formula ȳ = (y.
5. In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression ( SSR - not to be confused with the residual sum of squares RSS or sum of squares of errors), is a quantity used in describing how well a model, often a regression model, represents the data being modelled

College GPA (Y-hat) of high school graduates/applicants The regression equation will do a better job of predicting College GPA (Y-hat) of the original sample because it factors in all the Idiosyncratic relationships (correlations) of the original sample. Shrinkage: Original R2 will be Larger than future R2 Yi is the actual observed value of the dependent variable, y-hat is the value of the dependent variable according to the regression line, as predicted by our regression model. What we want to get is a feel for is the variability of actual y around the regression line, ie, the volatility of ϵ. This is given by the distance yi minus y-hat Y-hat (ŷ) is the symbol that represents the predicted equation for a line of best fit in linear regression. The equation takes the form ŷ = a + bx where b is.. a)The difference between the actual value, y, and the fitted value, y-hat. b)The difference between the fitted value, y-hat, and the mean, y-bar. c)The difference between the actual value, y, and the mean, y-ba. d)The square of the difference between the fitted value, y-hat, and the mean, y-bar. Question Y = 3x and x= 2.6 estimated value of Y ( i.e. Y-hat ) = 7.8 but actual mean when it was calculated by you came up to Y-bar = 12.75 Attached image is just to give an idea of estimated points Y-hat (given in green) Vs actual points on mean Y-bar (given in red) Thus 7.8 is the probable value of Y when 12.75 is the actual mean of the given data.

a = y bar - b(x bar) What is the fitted value? y hat. What is the residual formula. observed - fitted. What is the residual plot? A scatter plot of residuals vs explanatory variables or fitted values. When the scatterplot is linear, what does the residual plot look like? Random scattering of points Notation used in the course. b 0 (b-zero): estimated sample y-intercept in a linear regression model (more generally, estimated value of y when all the predictors equal zero) β 0 (beta-zero): population y-intercept in a regression model. b 1 (b-one): estimated sample slope in a linear regression model (more generally, estimated sample. In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T 2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution

Y-hat= the predicted Y B= slope (predicted amount by which Y increases when X increases by 1 unit) A= y intercept (the predicted height of the line when X=0) sometimes has no meaning in the context intercept of the LSRL is a=y(bar) - b x(bar 10 PM - 2 AM Thurs, Fri, 10 PM - 3 AM Sat. Y Bar Bottle Service. Y Bar Guestlist. Y Bar Tickets. Voted Best Lounge in Chicago by the Chicago Scene Magazine for 2007 and 2008, Y Bar has been a famous destination for the elite and fashionable in River North. Known for its distinctively elite and fashionable ambience, this lounge is a stand. Y Hat: Definition. Y hat (written ŷ ) is the predicted value of y (the dependent variable) in a regression equation. It can also be considered to be the average value of the response variable. The regression equation is just the equation which models the data set. The equation is calculated during regression analysis y = dependent variable values, y_hat = predicted values from model, y_bar = the mean of y. The R ² value, also known as coefficient of determination, tells us how much the predicted data, denoted by y_hat, explains the actual data, denoted by y. In other words, it represents the strength of the fit, however it does not say anything about the model itself — it does not tell you if the model. a)The difference between the actual value, y, and the fitted value, y-hat. b)The difference between the fitted value, y-hat, and the mean, y-bar. c)The difference between the actual value, y, and the mean, y-ba. d)The square of the difference between the fitted value, y-hat, and the mean, y-bar. Question

### Answered: What is the difference between y hat bartleb

• us the predicted ground truth, while the TSS is computed.
• Hat Matrix - Puts hat on Y • We can also directly express the fitted values in terms of only the X and Y matrices and we can further define H, the hat matrix • The hat matrix plans an important role in diagnostics for regression analysis. write H on boar
• g over the letter. If you are not able to get the bar.
• ation= , Rsquared) ## Coefficient of deter
• How do I type statistical symbols like X-Bar (X̅) in Excel. I also would like to type Y-Bar, d-bar, and p-hat. I am using Mac Excel 16.29. Thanks, eddiev1002
• us their respective means, over the square of x,
• der, the plot looks like this: Metrics To Assess Model. We will investigate four key metrics: Sum of Squared Errors (SSE) Total Sum of Squares (SST) R^2. Adjusted R^2. First, the formulas: Keep in

### Introduction to Linear Regression - Galvanize Blo

Statology Study is the ultimate online statistics study guide that helps you understand all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student The process of fitting the best fit line is called linear regression. The idea behind finding the best fit line is based on the assumption that the data are scattered about a straight line. The criteria for the best fit line is that the sum of the squared errors (SSE) is minimized, that is made as small as possible $$S = \sqrt{\frac{\sum (\hat y -y)^2}{n-2}}$$ S represents, in the units of predicted variable, on average how far the actual values fall from prediction. Confidence intervals¶ ¶ Approximately 95% of predictions fall within $\pm 2 standard error$ of regression from regression line. Problems¶ ¶ Multicollinearity is when predictors are. The graph of the line of best fit for the third-exam/final-exam example is as follows: The least squares regression line (best-fit line) for the third-exam/final-exam example has the equation: ^y = −173.51+4.83x y ^ = − 173.51 + 4.83 x. Remember, it is always important to plot a scatter diagram first

### STAT 231 Regressio

• In this case, every coefficient of $\hat \beta$ is then a weighted average of the corresponding coefficient in $\hat \beta_1$ and $\hat \beta_2$. Intuition. To see the intuition behind above result, consider the picture below. There's 6 data points divided in two groups: the green and blue dots
• The Latin small letter x is used to represent a variable or coefficient. In algebra, x is often used to represent an unknown value. The symbol x is also used to represent the horizontal dimension in the 2D cartesian coordinate system. The combining macron character is used to draw a macron (horizontal bar) over the symbol it is combined with.
• Since the Panhard/J-Bar is such an important locating device it is critical that the hardware is solid. Any flex creates unpredictable variables resulting in a car that is erratic. The hoop style shown adds rigidity and creates a solid feel for the driver. Then we get into Panhard/J-Bar split and reverse split
• Plot of residuals vs. y_hat: Plot of residuals vs. observed y: Plot of residuals vs. time (may lead to discovery of time as an unknown blocking variable) Plot of residuals vs. factor levels (may lead to discovery of curvature with respect to factor levels
• Online Linear Regression Calculator. This page allows you to compute the equation for the line of best fit from a set of bivariate data: Enter the bivariate x,y data in the text box.x is the independent variable and y is the dependent variable.Data can be entered in two ways
• A slope of zero implies that y-hat is zero; hence, the regression variability is zero. In other words, as x increases y remains constant. The equation for the line becomes y=a. The more the data hugs the regression line, the smaller is the SSE and therefore, the bigger is the SSR relative to the total variability

### What does a Y bar mean in statistics? - Quor

1. Calculating the equation of the least-squares line. A stonemason wants to look at the relationship between the density of stones she cuts and the depth to which her abrasive water jet cuts them. The data show a linear pattern with the summary statistics shown below: Find the equation of the least-squares regression line for predicting the.
2. such that the resulting model would yield predicted values $$\hat{Y}$$ that are as close as possible to the observed response values Y. If the form f has been wisely chosen, a good model will result and that model will have the characteristic that the differences (residuals = Y - $$\hat{Y}$$) will be uniformly near zero
3. imized SSE
4. A NEGATIVE covariance means variable X will increase as Y decreases, and vice versa, while a POSITIVE covariance means that X and Y will increase or decrease together. If you think about it like a line starting from (0,0), NEGATIVE covariance will be in quadrants 2 and 4 of a graph, and POSITIVE will be in quadrants 1 and 3
5. 8.1 Gauss-Markov Theorem. The Gauss-Markov theorem tells us that when estimating the parameters of the simple linear regression model $$\beta_0$$ and $$\beta_1$$, the $$\hat{\beta}_0$$ and $$\hat{\beta}_1$$ which we derived are the best linear unbiased estimates, or BLUE for short. (The actual conditions for the Gauss-Markov theorem are more relaxed than the SLR model.

Correlation and regression calculator. Enter two data sets and this calculator will find the equation of the regression line and corelation coefficient. The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line Answers: Numerator is the total variation in y around its mean The denominator is the total variation in y around its mean Question 11 10 out of 10 points If the prediction from the regression is perfect then Selected Answer: y-hat(i) will equal y(i) and R-squared will be one Answers: y-hat(i) will equal y(i) and R-squared will be zero y(i. 4. y vs y hat values. 5. Least squares regression. Intro #3 is a 10 page file. The emphasis is using a TI 30 XS multi view calculator to find significant values. Assignment A is a 1 page 6 question file where the student makes scatter plots of data and restricts their tick marks to 5 on each axis. Assignment #1 is a 1 page 40 question file View Homework Help - hw3+s17 from STA STA 108 at University of California, Davis. HW3 Brief Solution HW 3: 2.22, 2.25, 2.29, 2.42, 2.51 It is mainly for checking numerical answers, only partial step Boat Trailer Center V-Guide Supports. This Bow V Guide Support is seen mounted to a cross beam towards the front of your trailer. Its intention is to catch the bow of the boat, support it, and guide it to the Bow stop. It will mount to the cross member with a 2 Hat Bracket and (2) Square U-Bolts. Most commonly the cross member will be a 3 x 3.

### Y is for Ys, Y-hats, and Residuals R-blogger

8 ALinear)Probabilistic)Model The)points(x1, y 1),),)(x n, y n))resulting)from)n independent) observationswill)then)be)scattered)about)the)true) regression)line: This image cannot currently be displayed Machine learning applications and best practices. MEMM Labeling Bias Conditional Random Field. CRFs avoid the label bias problem a weakness exhibited by Maximum Entropy Markov Models (MEMM) and eliminates 2 unreasonable assumption in HMM

### Residual plots (against y vs y hat) Statistics Help

R-squared is very low and our residuals vs. fitted plot reveals outliers and non-constant variance. A common fix for this is to log transform the data. Let's try that and see what happens: plot (lm (log (y)~x),which = 3) The diagnostic plot looks much better. Our assumption of constant variance appears to be met Y bar Yas Island Rotana. Yesterday at 5:06 AM ·. #Euro2020. 3 back-to-back matches on ultra large projector screen with both indoor and outdoor seating options. ⚽ ������. ������������ vs ������������ 5 pm Find the equation of the regression line y ^ = b 0 + b 1 x giving b 0 and b 1 to the nearest 10 t h. Then plot the data points and the regression line. The formulas for b 0 and b 1 are given below. b 1 = n ∑ x y - ∑ x ∑ y n ∑ x 2 - ( ∑ x) 2 b 0 = ∑ y - b 1 ∑ x n. Average Monthly Temperatures given in degrees F. Month

ML Engineer มี metrics ที่ใช้วัดความถูกต้องของโมเดลหลายตัวมากดังนั้นเราจึงทำการ. The graph of the line of best fit for the third-exam/final-exam example is as follows: Figure 12.4. 3. The least squares regression line (best-fit line) for the third-exam/final-exam example has the equation: (12.4.3) y ^ = − 173.51 + 4.83 x. REMINDER. Remember, it is always important to plot a scatter diagram first y x rs b r r s Since r can never be larger than 1, the numerator indicates that the predicted y tends to be closer to the mean (in standard deviations) the its corresponding x. This property is called regression to the mean. So, when x increases by 1SD, y increases by only r times 1SD. This is called regression to the mean The slope of this line is 0, and the y-intercept is the sample mean of Y, which is Y-bar. In a baseline model, the X and Y variables are assumed to have no relationship. This means that for predicting values of the response variable, the mean of the response, Y-bar, does not depend on the values of the X variable ### Details of Simple Linear Regression, Assessment, and

R SQUARED: SST, SSE AND SSR: From these Wikipedia definitions: \[\begin{align} \text{SST}_{\text{otal}} &= \color{red}{\text{SSE}_{\text{xplained}}}+\color{blue. 2.4.2 Estimates and Standard Errors. The simple linear regression model can be obtained as a special case of the general linear model of Section 2.1 by letting the model matrix X consist of two columns: a column of ones representing the constant and a column with the values of x representing the predictor. Estimates of the parameters, standard.

Interpreting models with log transformation. The slope coefficient for the log transformed model is 0.02, meaning the log price difference between paintings whose widths are one inch apart is predicted to be 0.02 log livres. l o g ( price for width x+1) − l o g ( price for width x) = 0.02. 51 / 61 Value. Returns a list containing values related to the most appropriate R2 for the given model (or NULL if no R2 could be extracted). See the list below: Logistic models: Tjur's R2 General linear models: Nagelkerke's R2 Multinomial Logit: McFadden's R2 Models with zero-inflation: R2 for zero-inflated models Mixed models: Nakagawa's R2 Bayesian models: R2 baye

4.5.1. t. -Test. By assumption, the residuals are normally distributed, so the Z -test statistic could evaluate the parameter estimators, Z = ˆβ − β0 √σ2(X ′ X) − 1. where β0 is the null-hypothesized value, usually 0. σ is unknown, but ˆσ2 ( n − k) σ2 ∼ χ2. The ratio of the normal distribution divided by the adjusted chi. Statistics notation is very easy in Rmarkdown. Below a list of common components of statistics notation for reference. To leave a comment for the author, please follow the link and comment on their blog: simpleblog. R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics

### Symbol Sheet / SW

Here, y-hat is the fitted value for observation i and y-bar is the mean of Y. We don t necessarily discard a model based on a low R-Squared value. To compare the efficacy of two different regression models, it's a good practice to use the validation sample to compare the AIC of the two models Simple linear regression is univariate. One independent and one dependent. Assume data generated is linear. y = observed value, y (hat) = estimated value, y (bar) = average, e = errors, n = sample size. Least Squared Errors ~> This is the most commonly used estimation method and has the best properties. Value from 0 to 1 Therefore, you just have to know the true y values, the estimated y-hat values, and the mean of the true y values, y-bar. Share. Follow answered Jun 21 '17 at 18:07. Scratch'N'Purr Scratch'N'Purr. 6,700 1 1 gold badge 24 24 silver badges 37 37 bronze badges. 4 Ten pairs of data yield r = 0.168 and the regression equation y-hat = 9x+6. Also, y-bar = -9.9. a) What is the best predicted value of y for x = 7? b) In testing for a correlation between two varia..

$$accuracy = \frac{(y - \hat{y})^2}{\sum{_i}^n(y-\bar{y})^2}$$ Code. Let us put together the information we collected above and create the Regressor class Correlation (r) = .94. It is customary to talk about the regression of Y on X, hence the regression of weight on height in our example. The regression equation of our example is Y = -316.86 + 6.97X, where -361.86 is the intercept ( a) and 6.97 is the slope ( b ). We could also write that weight is -316.86+6.97height

y #y + #u z #z! ˜ p= #p #x e ˆ x + #p #y e ˆ y + #p #z e ˆ z Index Notation Also called Einstein Notation, this is the natural language for describing vectors, tensors, and fluid mechanics. The order of a tensor is equal to the number of unrepeated indices in the subscript (e.g., the matrix A ij has two unrepeated indices) and repeated indice Chapter 25 An Introduction to Linear Mixed Models. This chapter is very loosely based on materials from Chapters 25 and 26 of the Kleinbaum et al., textbook, also gathering information from several other sources to try to provide a basic introduction to linear mixed models.If STA 566/666 is offered in the future with me as an instructor, I would cover linear mixed models in more detail and go. The predicted distance (Y-hat) is now 343.54 cm, the predicted standard deviation (S-hat) is 3.3771. The Prediction Interval (PI) is from 333 to 353 cm. The prediction interval is the range in which you expect most of the validations runs to occur

σ 2 = E [ ( X − μ) 2]. Thus, the variance itself is the mean of the random variable Y = ( X − μ) 2. This suggests the following estimator for the variance. σ ^ 2 = 1 n ∑ k = 1 n ( X k − μ) 2. By linearity of expectation, σ ^ 2 is an unbiased estimator of σ 2. Also, by the weak law of large numbers, σ ^ 2 is also a consistent. Title: Linear Regression Worksheet Author: Larry Winner Last modified by: winner Created Date: 4/6/2007 12:16:00 PM Company: University of Florida Other title Correlation. A correlation measures three characteristics of the association between X and Y: The direction of the relation. A positive correlation (+) emerges when two variables are moving in the same direction. If the value of X increases (for example the length of a person), the value of Y also increased (for example the weight of a person) RSS = n ∑ i = 1(yi − ˆy)2. TSS = n ∑ i = 1(yi − ˉy)2. TSS will be constant regardless of the model being fit, and so maximizing ˉR2 is equivalent to minimizing RSS / (n − p − 1). The fact that RSS will always decrease as variables are added to the model explains why R2 always increases with additional variables 2.3.1 Interpretation of OLS estimates. A slope estimate $$b_k$$ is the predicted impact of a 1 unit increase in $$X_k$$ on the dependent variable $$Y$$, holding all other regressors fixed.In other words, if $$X_k$$ increases by 1 unit of $$X_k$$, then $$Y$$ is predicted to change by $$b_k$$ units of $$Y$$, when all other regressors are held fixed.. It is very important to recognize that.

This closeness can be measured by the length of the vector $\hat{Y}-\bar{Y} \cdot 1$. The square of a vector's length is the sum of its elements squared. These quantities are usually referred to as sums of squares Estimation in R: lm (Y ~ X1 + X2 + X1:X2, data) or, as a shortcut: lm (Y ~ X1 * X2) where * means all possible main effects and interactions of X1 and X2. The term associated with β3 is an interaction term, where the predictor is the product of predictor values. Let's now show that the above GLM gives us the two regression lines that. Span (ft) L y (in) Span (ft) L y (in) 8 48 1 5 60 10 6 0 2 0 8 0 12 7 2 25 75 15 6 0 3 0 72 4. Capacities listed in the Through-Fastened column are the allowable load for cases where one flange is through-fastened to deck or sheathing and the opposite flange is unbraced (uplift capacity for top flange through-fastened) Explained Variability (SSM) Distance from Regression Line to Mean Line: $$\Sigma(\hat{y}-\bar{y})^2$$ Unexplained Variability (SSE) Distance from Data Points to Regression Line: $$\Sigma(y_i-\hat{y})^2$$ As in ANOVA, if it's a good model, we expect more explained than un-explained variability and the proportion of the total variability.

A good way to visualize model performance is to plot $$y$$ vs. $$\hat{y}$$ - in other words, actual vs predicted. A perfect predictor would be a 45° diagonal through the origin; random guessing would be a shapeless or circular cloud of points This is a practical, empirical question, not a theoretical one that can be solved by mathematics. One way to answer it is to start from what Reynolds number means physically: it represents the ratio between typical inertia forces and viscous forces in the flow field How to find the correlation coefficient. Example. Using the data set from the last section, find the correlation coefficient. First, we need to find both means, x ¯ \bar x x ¯ and y ¯ \bar y y ¯ , x ¯ = 0 + 2 + 4 + 6 + 8 + 1 0 + 1 2 7 = 4 2 7 = 6 \bar x=\frac {0+2+4+6+8+10+12} {7}=\frac {42} {7}=6 x ¯ = 7 0 + 2 + 4 + 6 + 8 + 1 0 + 1 2 = 7. 10.1.0.1 Scatter plot. A scatter plot is a two dimensional graph of pairs of points from two numerical variables; In a quantitative bi-variate dataset, we have a $$(x,y)$$ pair for each sampling unit, where $$x$$ denotes the independent variable and $$y$$ denotes the dependent variable.; Each $$(x,y)$$ pair can be considered as a point on the Cartesian plan..

Finding the slope and intercept of the least squares regression line. The least squares regression line for predicting y y based on x x can be written as: ^y = a+bx. y ^ = a + b x. b= rsy sx ¯y = a+b¯x b = r s y s x y ¯ = a + b x ¯. We first find b, b, the slope, and then we solve for a, a, the y y -intercept. ������. Checkpoint 8.2.3 Then substitute these values in regression equation formula Regression Equation(y) = a + bx = -7.964 + 0.188x Suppose if we want to calculate the approximate y value for the variable x = 64 then, we can substitute the value in the above equation Regression Equation(y) = a + bx = -7.964 + 0.188(64) = 4.06 y.A y x Resultant force: Over a body of constant thickness in x and y W n i F z W i 1 W dW Location: x, y is the equivalent location of the force W from all W i's over all x & y locations (with respect to the moment from each force) from: M x W xW n i y i i 1 W W xdW x xdW x OR W x W x M y W y W n i x i i 1 W 1 Answer1. Active Oldest Votes. 2. Formulas can be checked against infinite online resources, not here. The most widespread use of x and X to distinguish something, is when it is needed to emphasize what is treated in theoretical derivations as a realized value (a fixed number, x ), and what as a random variable, X