Elementary Statistics: Finding the Sum of the Squared Residuals on TI-83-84. Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model).In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean. And also, the residuals have constant variance. It has been updated to reflect the use of Python in EGR 103. Step 1: Fit a model, save predicted and residual values. 1.1. P&ID PIP Sample Drawing. Least-squares technique THE SYMBOLS USED IN SIMPLE LINEAR REGRESSION The simple linear regression model is Y i = 0 + 1 x i + i for i = 1, 2, , n.The i values are assumed to constitute a sample from a population that has mean 0 and standard deviation (or sometimes ).The data will be (x1, Y 1), (x 2, Y 2), ., (x n, Y n).
e = y - e = y y ^. What the pattern may indicate. Assess model fit. Sample . If the model is correct, then they may sometimes be a fairly good estimate. The left side of the tilde symbol specifies the target variable (also called dependent variable or outcome) and the right side of the tilde specifies the predictor variable(s) (also called independent variables).. Let's move on to some R codes in action. Residual (Standardised Residual) subheading. Use the histogram of the residuals to determine whether the data are skewed or include outliers. In practice, residuals are used for three different reasons in regression: 1. To sum up standardized residuals. Step 3: - Check the randomness of the residuals. The patterns in the following table may indicate that the model does not meet the model assumptions. In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations of predicted from actual empirical values of data). Indeed. Ne w York: W.H. and notice how point is units above the line: Created with Raphal. Now if we wanted to know when this residual is positive and when it's negative it's pretty clear because it's just a basic subtraction. Enter the numbers in two statistics lists. It is important to examine the residual plot to look for any potential problems. A bar that is far away from the other bars. Semi-interquartile range A residual is a measure of how well a line fits an individual data point. . A residual (or error) is the difference between the predicted value of your data and the actual value of your data. - The F-value is the Mean Square Regression (2385.93019) divided by the Mean Square Residual (51.0963039), yielding F=46.69. 8. Scroll through your results until you find the box headed Residual Statistics. The data reported are for associations . Statistics and Probability. (Split the set of residuals into an upper half and lower half. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. Often we denote a residual with the lower case letter. . Scroll down and select RESID. In statistics, a residual refers to the amount of variability in a dependent variable (DV) that is "left over" after accounting for the variability explained by the predictors in your analysis (often a regression). Statistics and Probability; Statistics and Probability questions and answers "r " is the abbreviated symbol for which of the following regression statistics? Word in Definition. Residual Sum of Squares (RSS) is defined and given by the following function: max. From the above residual plot, we could infer that the residuals didn't form any pattern. Use of residuals. 7.3 - Overdispersion. Analysis of residuals allows you to estimate the adequacy of a model for particular data; it is widely used in regression analysis. The residual is the the difference between the observed value and the fitted value that the model predicts for each observation. A plot of the residual, leverage or the Cook's distance against the corresponding observation number (row, i or index) in the dataset is known as an Index Plot in statistics. Created with Raphal. Probability and statistics both employ a wide range of Greek/Latin-based symbols as placeholders for varying objects and quantities. SYMBOLS; SYNONYMS; USZIP; Search. Overdispersion occurs because the mean and variance . Extract the estimated standard deviation of the errors, the "residual standard deviation" (misnamed also "residual standard error", e.g., in summary.lm () 's output, from a fitted model). Look at the Minimum and Maximum values next to Std. Underlined text, printed URLs, and the table of contents become live links on screen; and you can use your browser's commands to change the size of the text or search for key words. 9391580295. XM Services. Particularly for the residuals: $$ \frac{306.3}{4} = 76.575 \approx 76.57 $$ 1 Starting With Matlab 2 Creating Arrays 3 Mathematical Operations With Arrays 4 Using Script Files And Managing Data 5 Two-dimensional Plots 6 Programming In Matlab 7 User-defined Functions And Function Files 8 Polynomials, Curve Fitting, And Interpolation . Hydraulic Sample Drawing. There are two ways to add the residuals to a list. The Akaike information criterion (AIC) is a mathematical method for evaluating how well a model fits the data it was generated from. Residual Variance. Whether you want to increase customer loyalty or boost brand perception, we're here for your success with everything from program design, to implementation, and fully managed services. To calculate the residual at the points x = 5, we subtract the predicted value from our observed value. Residuals. Residuals appear in many areas in mathematics, including iterative solvers such as the generalized minimal residual method, which seeks solutions to equations by systematically minimizing the residual. Measures how many standard deviations a value is from the mean. We're going to get a residual equal to zero. Residual Sum of Squares (RSS) is defined and given by the following function: At time zero, the predicted distance is 0.34 miles. Often, delta is considered the difference between a start and end value . If the minimum value is equal or below -3.29, or the maximum value is equal or above 3.29 then you have outliers.
Skewness. Areas with irregular water-bottom topography in shallow water (less than 25 m), and areas with rapidly varying velocity in the sediments near the . Freeman & Co, 5th edition. For every 1 change in x, the predicted y increases or decreases by this amount. Residuals measure the impact of firm-specific events during a particular period. This page is specifically for people in EGR 103 and represents a concordance of sorts among the lectures and the two textbooks with respect to different symbols for statistical quantities. X, Y, Z, T. Random variables. Certainly the residuals are some sort of estimators of (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). [2nd] "list" [ENTER]. Published on March 26, 2020 by Rebecca Bevans . Consider this simple data set with a line of fit drawn through it. E ( X 1 + X 2) =. 2. Tilde Symbol Explained. The extra variability not predicted by the generalized linear model random component reflects overdispersion. What does residual mean? Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and . This value falls on the Y-axis of the scatterplot. Math. XM Services. Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57 If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Author: Amos Gilat. For data points above the line, the residual is positive, and for . statistics, the science of collecting, analyzing, presenting, and interpreting data. Statistical Symbols; FAQs & Knowledge Base; . VARIANCE: Mean of Square Errors, symbolized s-squared or MSE, is equal to the sum of the residuals, symbolized by e-sub-I, squared then divided by the number of data points subtracted by two. Generalized linear models include binary regression and Poisson regression. So are actual values for and are predicted values for. Correlation coefficient D). Meaning of residual. See http://www.mathheals.com for more videos In general, the index k is used to mean the k th data point (out of N data . Problem. Regression can predict the sales of the companies on the basis of previous sales, weather, GDP growth, and other kinds of conditions.
The resulting scatterplot reveals that the unusual grouping of points noted in the residuals by predicted values scatterplot have large values for factor score 1; that is, they are high-priced vehicles. Once we produce a fitted regression line, we can calculate the residuals sum of squares (RSS), which is the sum of all of the squared residuals. Residual statics corrections usually are discussed in terms of applications to land data. The residual plot of residuals versus order should look random. Residuals are zero for points that fall exactly along the regression line. You can find residuals using the following equation. Residual (prediction error) The difference between a person's actual score and predicted score . If these assumptions are satisfied, then ordinary least squares regression will produce unbiased coefficient . Whether you want to increase customer loyalty or boost brand perception, we're here for your success with everything from program design, to implementation, and fully managed services. To demonstrate residual resampling, I will use procedures in Base SAS and SAS/STAT. Pneumatic Sample Drawing. Step 2: - Draw the residual plot graph. 26. JIC / NFPA Sample Drawing. the use of the third and the fourth scenarios affects the statistical efficiency of parameter estimates and leads to difficulty in interpreting the analytic . The sum of all of the residuals should be zero. Cornell Statistical Consulting Unit interested in determining whether or not the number of individuals with blue eyes and blond hair Since the adjusted Pearson residuals are normally distributed, those cells with absolute values greater than the critical value (0,1)=1.96 will have raw p-values of less than 0.05 (for a For a linear regression equation, y = 0.34 + 54.2x where x represents time and y represents distance, the y-int interpretation says. In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations of predicted from actual empirical values of data). Learn more about Minitab 18. e = y y ^. A raw residual is the difference between an observed value and a predicted value in a regression or other relevant statistical tool. A standardized residual is the raw residuals divided by an overall standard deviation of the raw residuals. (1) Part of stock returns not explained by the explanatory variable (the market index return). Residual. In statistics, AIC is used to compare different possible models and determine which one is the best fit for the data. The mean and the sum of the residuals are always equal to zero, and the value is positive if the data point is above the graph and negative if below it. h. F and Sig. Many times data admit more variability than expected under the assumed distribution. Extensions of this technique cover situations with more than one experimental variable or to non-linear regression situations, such as polynomial . "Residual" in statistics refers to the difference between the calculated value of the dependent variable against a predicted value. Statistics symbols you need to know. Plot the standardized residual of the simple linear regression model of the data set faithful against the independent variable waiting. Revised on May 25, 2022. X R2 2 p r s p s2 None of the above / does not have a symbol. We apply the lm function to a formula that describes the variable eruptions by the variable waiting, and save the linear regression model in a new variable . And that gives us our residual. . Q3 (the third quartile) 25. References The true relationship is linear. Delta is the overall change in a value. Statistics Symbols. The chi-square statistics were significant, indicating that there is an association among the variables, but the table is larger than 2x2 I had requested the adjusted standardized residuals from among the options in the Cells dialog (or /CELLS subcommand). (j) How many manatee deaths would you expect for a million power-boat registrations? Right about now you are probably thinking: "this guy likes the word "variability" way too much, he should buy a thesaurus already!" . ISBN: 9781119256830. Multiple linear regression: Y = a + b 1 X 1 + b 2 X 2 + b 3 X 3 + + b t X t + u. For real-world data, 0.94 is a pretty strong correlation. Know the meaning of high, moderate, low, positive, and negative correlation, and be able to recognize each from a graphs or verbal description of data. Examining residual plots helps you determine whether the ordinary least squares assumptions are being met. subset .
In practice sometimes this sum is not exactly zero. At 110 feet, a diver could dive for only five minutes. A residual plot is a graph that is used to examine the goodness-of-fit in regression and ANOVA. Let's suppose therefore. World-class advisory, implementation, and support services from industry experts and the XM Institute. Example /RESID=DEFAULT ID(SVAR) DEFAULT produces the default residuals statistics: Durbin-Watson statistic, a normal probability plot and histogram of ZRESID, and an outlier listing for ZRESID. [STAT] [1] . Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. use bold type for vector and matrix symbols; use italics for all other statistical symbols; Mathematical Copy For ease of reading, use spaces between elements in a mathematical expression (a + b = c), except in the case of a minus sign indicating a negative number which uses a space before the minus but not between the minus and the numeral. Example. Introduction to the Basic Practice of Statistics. To review, open the file in an editor that reveals hidden Unicode characters. Statistics and Probability questions and answers. e. e e. Calculating residuals is easy. However, in certain cases, residual statics corrections have produced dramatic improvement in marine data. 9391580296. So, the residuals are independent of each other. The 75 percentile. The general formula of these two kinds of regression is: Simple linear regression: Y = a + bX + u. . Thomas Barwick/Stone/Getty Images. Coefficient of determination B). Use the proper symbol. Sample Drawings. Sampling distribution . As pattern is quite random which indicates . View or Print: These pages change automatically for your screen or printer. The lower the RSS, the better the regression model fits the data. A . (2 . This vertical distance is known as a residual. The equation to approximate regression is referred to as y-hat, the letter y with a caret (^) on top. 1 Dispersion and deviance residuals For the Poisson and Binomial models, for a GLM with tted values ^ = r( X ^) the quantity D +(Y;^ ) can be expressed as twice the di erence between two maximized log-likelihoods for Y i indep P i: The rst model is the saturated model, i.e. I'll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results. Regression models. These assumptions are essentially conditions that should be met before we draw inferences regarding the model estimates or before we use a model to make a prediction.
The highest number in a set of data. World-class advisory, implementation, and support services from industry experts and the XM Institute. This distance is the RESIDUAL of y i, the difference between the predicted and observed values for this data point. Residual C). Introduction. A fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.
e = y - e = y y ^. What the pattern may indicate. Assess model fit. Sample . If the model is correct, then they may sometimes be a fairly good estimate. The left side of the tilde symbol specifies the target variable (also called dependent variable or outcome) and the right side of the tilde specifies the predictor variable(s) (also called independent variables).. Let's move on to some R codes in action. Residual (Standardised Residual) subheading. Use the histogram of the residuals to determine whether the data are skewed or include outliers. In practice, residuals are used for three different reasons in regression: 1. To sum up standardized residuals. Step 3: - Check the randomness of the residuals. The patterns in the following table may indicate that the model does not meet the model assumptions. In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations of predicted from actual empirical values of data). Indeed. Ne w York: W.H. and notice how point is units above the line: Created with Raphal. Now if we wanted to know when this residual is positive and when it's negative it's pretty clear because it's just a basic subtraction. Enter the numbers in two statistics lists. It is important to examine the residual plot to look for any potential problems. A bar that is far away from the other bars. Semi-interquartile range A residual is a measure of how well a line fits an individual data point. . A residual (or error) is the difference between the predicted value of your data and the actual value of your data. - The F-value is the Mean Square Regression (2385.93019) divided by the Mean Square Residual (51.0963039), yielding F=46.69. 8. Scroll through your results until you find the box headed Residual Statistics. The data reported are for associations . Statistics and Probability. (Split the set of residuals into an upper half and lower half. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. Often we denote a residual with the lower case letter. . Scroll down and select RESID. In statistics, a residual refers to the amount of variability in a dependent variable (DV) that is "left over" after accounting for the variability explained by the predictors in your analysis (often a regression). Statistics and Probability; Statistics and Probability questions and answers "r " is the abbreviated symbol for which of the following regression statistics? Word in Definition. Residual Sum of Squares (RSS) is defined and given by the following function: max. From the above residual plot, we could infer that the residuals didn't form any pattern. Use of residuals. 7.3 - Overdispersion. Analysis of residuals allows you to estimate the adequacy of a model for particular data; it is widely used in regression analysis. The residual is the the difference between the observed value and the fitted value that the model predicts for each observation. A plot of the residual, leverage or the Cook's distance against the corresponding observation number (row, i or index) in the dataset is known as an Index Plot in statistics. Created with Raphal. Probability and statistics both employ a wide range of Greek/Latin-based symbols as placeholders for varying objects and quantities. SYMBOLS; SYNONYMS; USZIP; Search. Overdispersion occurs because the mean and variance . Extract the estimated standard deviation of the errors, the "residual standard deviation" (misnamed also "residual standard error", e.g., in summary.lm () 's output, from a fitted model). Look at the Minimum and Maximum values next to Std. Underlined text, printed URLs, and the table of contents become live links on screen; and you can use your browser's commands to change the size of the text or search for key words. 9391580295. XM Services. Particularly for the residuals: $$ \frac{306.3}{4} = 76.575 \approx 76.57 $$ 1 Starting With Matlab 2 Creating Arrays 3 Mathematical Operations With Arrays 4 Using Script Files And Managing Data 5 Two-dimensional Plots 6 Programming In Matlab 7 User-defined Functions And Function Files 8 Polynomials, Curve Fitting, And Interpolation . Hydraulic Sample Drawing. There are two ways to add the residuals to a list. The Akaike information criterion (AIC) is a mathematical method for evaluating how well a model fits the data it was generated from. Residual Variance. Whether you want to increase customer loyalty or boost brand perception, we're here for your success with everything from program design, to implementation, and fully managed services. To calculate the residual at the points x = 5, we subtract the predicted value from our observed value. Residuals. Residuals appear in many areas in mathematics, including iterative solvers such as the generalized minimal residual method, which seeks solutions to equations by systematically minimizing the residual. Measures how many standard deviations a value is from the mean. We're going to get a residual equal to zero. Residual Sum of Squares (RSS) is defined and given by the following function: At time zero, the predicted distance is 0.34 miles. Often, delta is considered the difference between a start and end value . If the minimum value is equal or below -3.29, or the maximum value is equal or above 3.29 then you have outliers.
Skewness. Areas with irregular water-bottom topography in shallow water (less than 25 m), and areas with rapidly varying velocity in the sediments near the . Freeman & Co, 5th edition. For every 1 change in x, the predicted y increases or decreases by this amount. Residuals measure the impact of firm-specific events during a particular period. This page is specifically for people in EGR 103 and represents a concordance of sorts among the lectures and the two textbooks with respect to different symbols for statistical quantities. X, Y, Z, T. Random variables. Certainly the residuals are some sort of estimators of (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). [2nd] "list" [ENTER]. Published on March 26, 2020 by Rebecca Bevans . Consider this simple data set with a line of fit drawn through it. E ( X 1 + X 2) =. 2. Tilde Symbol Explained. The extra variability not predicted by the generalized linear model random component reflects overdispersion. What does residual mean? Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and . This value falls on the Y-axis of the scatterplot. Math. XM Services. Df Sum Sq Mean Sq F value Pr(>F) Model 1 37.0 37.00 0.483 0.525 Residuals 4 306.3 76.57 If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of freedom, you get the mean square. Author: Amos Gilat. For data points above the line, the residual is positive, and for . statistics, the science of collecting, analyzing, presenting, and interpreting data. Statistical Symbols; FAQs & Knowledge Base; . VARIANCE: Mean of Square Errors, symbolized s-squared or MSE, is equal to the sum of the residuals, symbolized by e-sub-I, squared then divided by the number of data points subtracted by two. Generalized linear models include binary regression and Poisson regression. So are actual values for and are predicted values for. Correlation coefficient D). Meaning of residual. See http://www.mathheals.com for more videos In general, the index k is used to mean the k th data point (out of N data . Problem. Regression can predict the sales of the companies on the basis of previous sales, weather, GDP growth, and other kinds of conditions.
The resulting scatterplot reveals that the unusual grouping of points noted in the residuals by predicted values scatterplot have large values for factor score 1; that is, they are high-priced vehicles. Once we produce a fitted regression line, we can calculate the residuals sum of squares (RSS), which is the sum of all of the squared residuals. Residual statics corrections usually are discussed in terms of applications to land data. The residual plot of residuals versus order should look random. Residuals are zero for points that fall exactly along the regression line. You can find residuals using the following equation. Residual (prediction error) The difference between a person's actual score and predicted score . If these assumptions are satisfied, then ordinary least squares regression will produce unbiased coefficient . Whether you want to increase customer loyalty or boost brand perception, we're here for your success with everything from program design, to implementation, and fully managed services. To demonstrate residual resampling, I will use procedures in Base SAS and SAS/STAT. Pneumatic Sample Drawing. Step 2: - Draw the residual plot graph. 26. JIC / NFPA Sample Drawing. the use of the third and the fourth scenarios affects the statistical efficiency of parameter estimates and leads to difficulty in interpreting the analytic . The sum of all of the residuals should be zero. Cornell Statistical Consulting Unit interested in determining whether or not the number of individuals with blue eyes and blond hair Since the adjusted Pearson residuals are normally distributed, those cells with absolute values greater than the critical value (0,1)=1.96 will have raw p-values of less than 0.05 (for a For a linear regression equation, y = 0.34 + 54.2x where x represents time and y represents distance, the y-int interpretation says. In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations of predicted from actual empirical values of data). Learn more about Minitab 18. e = y y ^. A raw residual is the difference between an observed value and a predicted value in a regression or other relevant statistical tool. A standardized residual is the raw residuals divided by an overall standard deviation of the raw residuals. (1) Part of stock returns not explained by the explanatory variable (the market index return). Residual. In statistics, AIC is used to compare different possible models and determine which one is the best fit for the data. The mean and the sum of the residuals are always equal to zero, and the value is positive if the data point is above the graph and negative if below it. h. F and Sig. Many times data admit more variability than expected under the assumed distribution. Extensions of this technique cover situations with more than one experimental variable or to non-linear regression situations, such as polynomial . "Residual" in statistics refers to the difference between the calculated value of the dependent variable against a predicted value. Statistics symbols you need to know. Plot the standardized residual of the simple linear regression model of the data set faithful against the independent variable waiting. Revised on May 25, 2022. X R2 2 p r s p s2 None of the above / does not have a symbol. We apply the lm function to a formula that describes the variable eruptions by the variable waiting, and save the linear regression model in a new variable . And that gives us our residual. . Q3 (the third quartile) 25. References The true relationship is linear. Delta is the overall change in a value. Statistics Symbols. The chi-square statistics were significant, indicating that there is an association among the variables, but the table is larger than 2x2 I had requested the adjusted standardized residuals from among the options in the Cells dialog (or /CELLS subcommand). (j) How many manatee deaths would you expect for a million power-boat registrations? Right about now you are probably thinking: "this guy likes the word "variability" way too much, he should buy a thesaurus already!" . ISBN: 9781119256830. Multiple linear regression: Y = a + b 1 X 1 + b 2 X 2 + b 3 X 3 + + b t X t + u. For real-world data, 0.94 is a pretty strong correlation. Know the meaning of high, moderate, low, positive, and negative correlation, and be able to recognize each from a graphs or verbal description of data. Examining residual plots helps you determine whether the ordinary least squares assumptions are being met. subset .
In practice sometimes this sum is not exactly zero. At 110 feet, a diver could dive for only five minutes. A residual plot is a graph that is used to examine the goodness-of-fit in regression and ANOVA. Let's suppose therefore. World-class advisory, implementation, and support services from industry experts and the XM Institute. Example /RESID=DEFAULT ID(SVAR) DEFAULT produces the default residuals statistics: Durbin-Watson statistic, a normal probability plot and histogram of ZRESID, and an outlier listing for ZRESID. [STAT] [1] . Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. use bold type for vector and matrix symbols; use italics for all other statistical symbols; Mathematical Copy For ease of reading, use spaces between elements in a mathematical expression (a + b = c), except in the case of a minus sign indicating a negative number which uses a space before the minus but not between the minus and the numeral. Example. Introduction to the Basic Practice of Statistics. To review, open the file in an editor that reveals hidden Unicode characters. Statistics and Probability questions and answers. e. e e. Calculating residuals is easy. However, in certain cases, residual statics corrections have produced dramatic improvement in marine data. 9391580296. So, the residuals are independent of each other. The 75 percentile. The general formula of these two kinds of regression is: Simple linear regression: Y = a + bX + u. . Thomas Barwick/Stone/Getty Images. Coefficient of determination B). Use the proper symbol. Sample Drawings. Sampling distribution . As pattern is quite random which indicates . View or Print: These pages change automatically for your screen or printer. The lower the RSS, the better the regression model fits the data. A . (2 . This vertical distance is known as a residual. The equation to approximate regression is referred to as y-hat, the letter y with a caret (^) on top. 1 Dispersion and deviance residuals For the Poisson and Binomial models, for a GLM with tted values ^ = r( X ^) the quantity D +(Y;^ ) can be expressed as twice the di erence between two maximized log-likelihoods for Y i indep P i: The rst model is the saturated model, i.e. I'll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results. Regression models. These assumptions are essentially conditions that should be met before we draw inferences regarding the model estimates or before we use a model to make a prediction.
The highest number in a set of data. World-class advisory, implementation, and support services from industry experts and the XM Institute. This distance is the RESIDUAL of y i, the difference between the predicted and observed values for this data point. Residual C). Introduction. A fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.