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[DOC File]Assumptions for Linear Regression
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SSR Sum Squares Regression – Explained Variation – Variation of the predicted values from the mean – Variation than can be attributed to the relationship between X and Y. SST = SSR + SSE. R2 = F = F is the ratio of explained variation to unexplained variation. If more variation is explained, F>1. Use the F table to check significance.
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[DOC File]Simple Linear Regression: Computational Aspects
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R2 = (SSyy - SSE) / SSyy = 1 – (SSE / SSyy), 0 R2 1 . The numerical value of R2 represents the proportion of the sum of squares of deviations of the y values about their mean that can be attributed to the linear relationship between y and x. For our numerical example, we have: R2 = (SSyy - SSE) / SSyy = (54 – 1.1) / 54 = 0.98
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[DOC File]Making a Scatterplot in R Commander
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Simple Linear Regression in R In order to do simple linear regression in R, you must first have a data table stored in R. Suppose the data for Problem 19 of Chapter One has been stored in an R object named Data which has two columns, the first column named GPA and the second column named ACT.
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[DOC File]Chapter 11 – Simple linear regression
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Procedure: First, take base 10 logarithms of Y and X1 and X2, and fit the linear regression model on the transformed variables. The relationship will be linear for the transformed variables. Case 2: Exponential Model (with multiplicative nonnegative errors) Taking natural logarithms of the Y values gives the model: Multicollinearity (Sec. 12-9)
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[DOC File]Derivation of the Ordinary Least Squares Estimator
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Multiple Regression Case. In the previous reading assignment the ordinary least squares (OLS) estimator for the simple linear regression case, only one independent variable (only one x), was derived. The procedure relied on combining calculus and algebra to minimize of the sum of squared deviations.
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[DOC File]Chapter 1 – Linear Regression with 1 Predictor
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Chapter 1 – Linear Regression with 1 Predictor. Statistical Model. where: is the (random) response for the ith case. are parameters . is a known constant, the value of the predictor variable for the ith case. ... (SSE). Also, the estimated variance is referred to as the .
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[DOC File]Serial Correlation in Regression Analysis
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The estimated regression parameters, a, b1, b2, . . . ,bk, remain unbiased estimators of the corresponding true values, A, B1, B2, . . ,Bk, leaving the estimated model appropriate for establishing point estimates of A, B, etc., and the model can be used for predicting values of Y for any given set of X values. ... Notice that the denominator of ...
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[DOC File]A fitted value is simply another name for a predicted ...
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SSE. is the total sum of squared deviations about the regression line . . SSR. is the total sum of squared deviations due to regression, i.e. SSR, however, is most easily found by computing the difference SSR = SST – SSE. Interpreting r2: Blank- percent of the variation in y variable is explained by the regression …
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[DOC File]CHAPTER FOURTEEN .tw
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38. In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is. a. 0.20. b. 1.67. c. 0.60. d. 0.40. 39. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4 X
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[DOC File]Derivation of the Ordinary Least Squares Estimator
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Simple Linear Regression Case. As briefly discussed in the previous reading assignment, the most commonly used estimation procedure is the minimization of the sum of squared deviations. This procedure is known as the ordinary least squares (OLS) estimator. ... SSE is the amount of variation not explained by the regression equation.
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Sse linear regression