Source df sum of squares mean squares f pr f acetic 1

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Source DF Sum of Squares Mean Squares F Pr > F ACETIC 1 0.56 0.56 0.0054 0.9419 H2S 1 1007.69 1007.69 9.8187 0.0042 LACTIC 1 533.26 533.26 5.1959 0.0311 The Lack of Fit Test When we want to determine whether a specified regression function adequately fits the data, we can conduct a lack of fit test. However, it is important to note that the test requires repeated observations (replications) for at least one of the values of the predictors ( X ). This test is also based on decomposing sums of squares (due to Errors) and the test procedure can be derived in the same way as testing the full vs. reduced model. F = (SSLF SSPE) / ( n p ( n c )) MSPE where p is the number of regression parameters and c is the number of distinct X values, SSLF denotes the lack of fit sum of squares, and SSPE (thus, MSPE for mean squares) stands for the sum of squares due to pure error. PAGE 35
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2.3 Qualitative Independent Variables c circlecopyrt HYON-JUNG KIM, 2017 2.3 Qualitative Independent Variables Types of variables Qualitative variables : Numerical measurements on the phenomena of interest are not possible. Rather, the observations are categorical. e.g. gender (female, male), Company status (private, public), Treatment (yes, no), blood pressure rating (low, average, high) Quantitative variables: The observations are in the form of numerical values. e.g. age, income, temperature, number of defectives, etc. Qualitative or “classification” variables can be included as explanatory variables in regression models by using indicator variables (also called ‘dummy’ or ‘binary’ variables). Example: On average, do smoking mothers have babies with lower birth weight? Response ( Y ): birth weight in grams of baby X 1 : length of gestation in weeks, X 2 : Smoking status of mother (smoker or non-smoker) Then, a first order model with one binary and one quantitative predictor appears to be a natural model to formulate for these data: Y i = β 0 + β 1 X i 1 + β 2 X i 2 + ǫ i , where X i 2 = 1 if mother i smokes 0 otherwise Q. Why not just fit two separate regression functions one for the smokers and one for the non-smokers? The combined regression model assumes that the slope for the two groups are equal and that the variances of the error terms are equal. Then, it is better to use as much data as possible to estimate standard errors of regression coefficients for testing and confidence intervals. Pooling your data and fitting the combined regression function allows you to easily and efficiently answer research questions concerning the binary predictor variable. PAGE 36
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2.3 Qualitative Independent Variables c circlecopyrt HYON-JUNG KIM, 2017 Example. If we are interested in quantifying the relationship between total population (of a metropolitan area) and number of active physicians it may be important to take (4) geographic regions into account. The indicator variables can be easily used to identify each of 4 regions as follows: X 1 = 1 if region 1 0 otherwise X 2 = 1 if region 2 0 otherwise X 3 = 1 if region 3 0 otherwise X 4 = 1 if region 4 0 otherwise
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