multiple linear regression pdf

endstream endobj 50 0 obj<> endobj 51 0 obj<> endobj 52 0 obj<>stream "�gxp�uI)\ns�73��s�� `Z!�W��?�!�K�n]�s��]�_�O�r7e|�jAY$�W08�4�Јt�4 ��J�T��/QWߴ�� :�hʜI˿@Y�%�lB�q��\��@�f]�yư�`�r��e��K破��;��_��]i��. 0000010194 00000 n ��2��̀�2�� `�x�ъa�>�5�@1b�Ȱ��a"�C3��L��?0~b�6�Gg�t$�L��f��taa� �d=�fbk�E��\�� U 0000003569 00000 n Multiple(linearregressioninJMP(1) Data(exploration:(Scatterplot(matrix#(datasetcase0902.jmp)# o Select“multivariate”#then#putall#variables#or#choose#some#of#them#iny: columns#box# To#determine#the#axes#of#the#scatterplotmatrix#you#mustexamine#the#diagonal# of#the#matrix.#The#column#in#the#plotdetermines#the#Xaxis,#while#the#plot’s#row# It does this by simply adding more terms to the linear regression equation, with each term representing the impact of a different physical parameter. . 0000008428 00000 n And, because hierarchy allows multiple terms to enter the model at any step, it is possible to identify an important square or interaction term, even if the associated linear term is … While simple linear regression only enables you to predict the value of one variable based on the value of a single predictor variable; multiple regression allows you to use multiple predictors. ��BC�K, �O��JH->��c��Y]��R �VQZ�2��3��ps��@��Y�U�� RS�}�B�".mCYD�7,0>z�nwx�j��=ܲ��!�M{�1w`cњ"�K�"S��z��S$-gR�I�zx m��C�on�b#?� BTb��U��zQ}&�85B�� N�G�$�d��cx�kFi��S"�J��ߵ�Z$�S��䓌�T2:h�A��J}Ri��w:��M]�9�J��\J8�fI��ɔԨ�s2L��B�6) '��żE��\��V�*[٭y�vگa�F��y�2O�FR!5OV~[�V��`щp�Ҍ�~i�a��>m��n��M��H� �*t��ܼ�\�F-Ա��:޶ �"�:.�il��#��iև��x� ��_��]�!M�B��? 0000051564 00000 n 0000009048 00000 n %%EOF 0000001503 00000 n x�b```f``)``c``:� Ȁ ��@Q�� 0000070583 00000 n 9.2.1) 1. If two of the independent variables are highly related, this leads to a problem called multicollinearity. 0000006371 00000 n Linear Regression vs. Xn). 0000004797 00000 n All the assumptions for simple regression (with one independent variable) also apply for multiple regression with one addition. 3 0 obj << H��TM��0��W��:�8��r�R��&U�eſgl�ۦ��6��yo��1{�+�$p�L(�8=iU�O+��>㰣��^��P=Cg�� (�� (�7��3�$�@#�(��t��C��K��z�k��86}�]&A,�ܠ� 4GCBPh|��z*��p��[�t&�XExȞ6E�E܌��v^��c�M�1��m�..��!Wa�S�bQ= ��D�X㺜��F��]�z��K6�s�%�6�t3�:"��y�z��w�n��}5l��!��w�M��t�3�"U#E��O=4��5�Y�Pw��1�Ah� q$��@k�=4��Aą��E�1��"#��lZ��JSH��1�v�%/��E�?TF��K*uAE$� `|��\b�d얌�\{qb��e��%��3C��x�î.mjm�a��:� ��7��,�^ܼ�s��ҍ�Њ��!��w~Y��(��e�e��=3ʠ��"yy[��eV#�q�v� H�� Multiple Regression Introduction Multiple Regression Analysis refers to a set of techniques for studying the straight-line relationships among two or more variables. The multiple regression model with all four predictors produced R² = .575, F(4, 135) = 45.67, p < .001. Thus, this is a test of the contribution of x j given the other predictors in the model. 0000006002 00000 n 0000084824 00000 n {3��?>3�-1~ㄔ@AӀ�A��3!�_�گAo}��s4�ЈP+��`��c[+��w��U7#va��7#ł'�}'�X�J� � 0000007345 00000 n Christensen: Log-Linear Models and Logistic Regression, Second Edition Creighton: A First Course in Probability Models and Statistical Inference Dean and Voss: Design and Analysis of Experiments du Toit, Steyn, and Stumpf: Graphical Exploratory Data Analysis Durrett: Essentials of Stochastic Processes 0000005274 00000 n + βXin + εi Where: Yi is the observed response of the ith individual, Xi1, Xi2, Xi3 Multiple Linear Regression Multiple linear regression allows you to determine the linear relationship between a dependent variable (Y) and a series of independent variables (X1, X2, X3, . In statistics, linear regression is a linear approach to modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables).The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This model generalizes the simple linear regression in two ways. Linear Regression as a Statistical Model 5. /Filter /FlateDecode . This model generalizes the simple linear regression in two ways. A sound understanding of the multiple regression model will help you to understand these other applications. Multiple Linear Regression Multiple linear regression allows you to determine the linear relationship between a dependent variable (Y) and a series of independent variables (X1, X2, X3, . H��TMo�0��W�( �/[P�]z6�mn��\��u��$�v�#1m?�=�Q��W6��3��vu� �+[�z��W�Z��z��% The linear model is: Y=β0 + β1Xi1 + β2Xi2 + β3Xi3 + . It is used to show the relationship between one dependent variable and two or more independent variables. Multiple Regression: An Overview . That is, the true functional relationship between y and xy x2,. 0000001423 00000 n Xn). All the assumptions for simple regression (with one independent variable) also apply for multiple regression with one addition. Assumptions for regression . 0000003835 00000 n Multiple linear regression. endstream endobj 59 0 obj<> endobj 60 0 obj<> endobj 61 0 obj<>stream . %PDF-1.3 H�TP�N�0��91$��`��KD{.qK$�Dn:��IJ{��lyn�[� ��a��c��ኣ'�48o��m�N&��n�N- �Z��p��Uu�N _�! ��S��"(�=�7�*b �K[��CQ��Fɗ�%w�lǬ��^�Cxe��~�R�F��\_�T2�� l��o2�P�=�|"3��!� �rOV�#[��%;߇�I�DYn��nL�}�G��0(:2�4�K�Ps6�+t��s��qANl�*��fw1�P�Q\LI%�z��u�ٚe]��On0h;�8�` �� Multiple Linear Regression is an analysis procedure to use whe n more than one explanatory variable is included in a “model”. 0000006928 00000 n That is, when we believe there is more than one explanatory variable that might help “explain” or “predict” the response variable, we’ll put all … 0000070170 00000 n hޒ�¥��Ղ�_� 'ws�� Y�3��`)䄒��BB��$��|M!˥Qb��H��;��³��}k^��-d��`Qyyr}oG;��>�ƨ]M>��^-/��k��$+*��$r�X@��l^އ�)�S��p�>��|⼌(#�`�+�j$ �XT�� endstream endobj 53 0 obj<> endobj 54 0 obj<> endobj 55 0 obj<>stream So from now on we will assume that n > p and the rank of matrix X is equal to … 0000004159 00000 n %PDF-1.4 %�� MULTIPLE REGRESSION 3 allows the model to be translated from standardized to unstandardized units. Multiple regression is an extension of linear regression models that allow predictions of systems with multiple independent variables. Multiple(linearregressioninJMP(1) Data(exploration:(Scatterplot(matrix#(datasetcase0902.jmp)# o Select“multivariate”#then#putall#variables#or#choose#some#of#them#iny: columns#box# To#determine#the#axes#of#the#scatterplotmatrix#you#mustexamine#the#diagonal# of#the#matrix.#The#column#in#the#plotdetermines#the#Xaxis,#while#the#plot’s#row# As in simple linear regression, under the null hypothesis t 0 = βˆ j seˆ(βˆ j) ∼ t n−p−1. Popular spreadsheet programs, such as Quattro Pro, Microsoft Excel, Multiple linear regression models are often used as empirical models or approximating functions. 37 0 obj <> endobj x��Zݏ��(�AFΌ�-�! MULTIPLE REGRESSION 3 allows the model to be translated from standardized to unstandardized units. 0000001056 00000 n In this blog post, I want to focus on the concept of linear regression and mainly on the implementation of it in Python. 0000070399 00000 n Thus, this is a test of the contribution of x j given the other predictors in the model. Multiple Linear Regression and Matrix Formulation. This growth emerges from the current technologies and the procedure that is directed towards improving student performance. Y is the dependent variable. We reject H 0 if |t 0| > t n−p−1,1−α/2. 37 38 View Week 3-2 Multiple Linear Regression.pdf from IS 4242 at National University of Singapore. Estimation, hypothesis testing, etc. Multiple linear regression needs at least 3 variables of metric (ratio or interval) scale. Multiple linear regression models are often used as empirical models or approximating functions. 0000002244 00000 n Multiple linear regression model is the most popular type of linear regression analysis. Assumptions for regression . . 0000000016 00000 n This chapter presents multiple linear regression, which is used when you have two or more independent variables and one dependent vari-able. Second, multiple regression is an extraordinarily versatile calculation, underly-ing many widely used Statistics methods. This is a partial test because βˆ j depends on all of the other predictors x i, i 6= j that are in the model. Multiple Linear Regression •Extension of the simple linear regression model to two or more independent variables! While simple linear regression only enables you to predict the value of one variable based on the value of a single predictor variable; multiple regression allows you to use multiple predictors. U9611 Spring 2005 3 Multiple Regression Data: Linear regression models (Sect. In fact, everything you know about the simple linear regression modeling extends (with a slight modification) to the multiple linear regression models. The sample must be representative of the population 2. . Multiple regression is like linear regression, but with more than one independent value, meaning that we try to predict a value based on two or more variables.. Take a look at the data set below, it contains some information about cars. 0000009620 00000 n �f#M 0000010708 00000 n H��Sێ�0}�+��2k��V�z�]5MՠJնl�$�@�tտ��m��X��3gfʛ ��b�\B�:`�P΃�9��G��]�Y+X�V�Up��/Q�=�S�gp�9-�x��n�r�{�כ �E�PEMC��f��m��~��Z�� Ex: Y: 1st year GPA, X Worked Example For this tutorial, we will use an example based on a fictional … C�Y��V��!Z�'xC�C��Ѥn8/�1'��5�A��U��hG77��z�Y35Ƿ m 0000063093 00000 n Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Multiple Linear Regression is an analysis procedure to use whe n more than one explanatory variable is included in a “model”. xref Multiple Linear Regression Model We consider the problem of regression when the study variable depends on more than one explanatory or independent variables, called a multiple linear regression model. >> Multiple Linear Regression Model We consider the problem of regression when the study variable depends on more than one explanatory or independent variables, called a multiple linear regression model. stream MULTIPLE LINEAR REGRESSION ANALYSIS USING MICROSOFT EXCEL by Michael L. Orlov Chemistry Department, Oregon State University (1996) INTRODUCTION In modern science, regression analysis is a necessary part of virtually almost any data reduction process. In simple linear regression this would correspond to all Xs being equal and we can not estimate a line from observations only at one point. Main focus of univariate regression is analyse the relationship between a dependent variable and one independent variable and formulates the linear relation equation between dependent and independent variable. Simple linear regression in SPSS resource should be read before using this sheet. y = "0 + "1 x 1 + "2 x 2 +...+" n x n +# •Partial Regression Coefﬁcients: β i ≡ effect on the dependent variable when increasing the ith independent variable by 1 … We reject H 0 if |t 0| > t n−p−1,1−α/2. proceeds as in the multiple regression model using OLS The coefficients are difficult to interpret, but the regression function itself is interpretable . That is, the true functional relationship between y and xy x2,. 0000002383 00000 n If two of the independent variables are highly related, this leads to a problem called multicollinearity. /Length 2711 Multiple Linear Regression The population model • In a simple linear regression model, a single response measurement Y is related to a single predictor (covariate, regressor) X for each observation. 1. 0000001682 00000 n endstream endobj 58 0 obj<>stream Multiple Linear Regression •Extension of the simple linear regression model to two or more independent variables! 0000008173 00000 n <<7BB326E122FDFA49B5DA0AD1ADBD118E>]>> 0000084358 00000 n 0000003309 00000 n 0000004083 00000 n endstream endobj 56 0 obj<> endobj 57 0 obj<>stream �o�M��# ��\ӝiw�0 =s=�ho.ʒ3 �%��|2��a$h�{�a�y�qRL�T��J�8�cY Bj~�X^��I��G��Co�R3~j?M��Y� L��"�E��o��`2��TkS�h_�P��;�If~� �Ӏ��>�?��(9� y = "0 + "1 x 1 + "2 x 2 +...+" n x n +# •Partial Regression Coefﬁcients: β i ≡ effect on the dependent variable when increasing the ith independent variable by 1 … Multiple linear regression. Multiple Regression. And, because hierarchy allows multiple terms to enter the model at any step, it is possible to identify an important square or interaction term, even if the associated linear term is … trailer Currently, there is rapid growth and development in the educational sector. 4. �Z�/�M��Akkwu�-W�oo��w�CʒL��]$@��p>~34_��V,�R��v�޾��+�*S�5�b%�f�KV1�3��Y�%��s��IeW7~��?��aɳz��j��d��궫��n��߉gNk$��`\-V�2�'{uh��H��K��o�ou�m��M� �W�]��2��J�O)��#��?��Ωk�� iM'h� ��2+�"��� hn�YAʎuA��QjaQ�7��n��Oa;z$��}Xg[��n ��/��1�M`��scq�d�&��he\�AՆ�ֵ�td'��h�� t�]��ׇ��!��E�?.��J\�.hCyTW��*p�cZ��0� �V(�W��u_u��-W�� Multiple regression estimates the β’s in the equation y =β 0 +β 1 x 1j +βx 2j + +β p x pj +ε j The X’s are the independent variables (IV’s). Linear Models Regression & Classification Vaibhav Rajan Department of Information Systems & Regression analysis is a common statistical method used in finance and investing.Linear regression is … That is, when we believe there is more than one explanatory variable that might help “explain” or “predict” the response variable, we’ll put all … In simple linear regression this would correspond to all Xs being equal and we can not estimate a line from observations only at one point. Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R (R Core Team 2020) is intended to be accessible to undergraduate students who have successfully completed a regression course through, for example, a textbook like Stat2 (Cannon et al. Introduction. This is just the linear multiple regression model – except that the regressors are powers of X! 0000005535 00000 n . The author and publisher of this eBook and accompanying materials make no representation or warranties with respect to the accuracy, applicability, fitness, or The linear model is: Y=β0 + β1Xi1 + β2Xi2 + β3Xi3 + . 0000006150 00000 n Worked Example For this tutorial, we will use an example based on a fictional … MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES In the previous chapter, simple linear regression was used when you have one indepen-dent variable and one dependent variable. 74 0 obj<>stream A rule of thumb for the sample size is that regression analysis requires at least 20 cases per independent variable in the analysis, in the simplest case of having just two independent variables that requires j� This is a partial test because βˆ j depends on all of the other predictors x i, i 6= j that are in the model. As can be seen in Table1, the Analytic and Quantitative GRE scales had significant positive regression weights, indicating students with higher scores on these scales were expected to have higher 1st year GPA, after controlling for the other startxref As in simple linear regression, under the null hypothesis t 0 = βˆ j seˆ(βˆ j) ∼ t n−p−1. So from now on we will assume that n > p and the rank of matrix X is equal to … 0000002919 00000 n 0000084623 00000 n �'�X�130~`(:�6n�RM/4��.�y��Ԑ�F�ewJ6�8��|��\�"�Sƙ;sc�T]v��Gg�l �#��r��D��E�إ��6�� 2%�"�J 6H Linear Regression Assumptions • Linear regression is a parametric method and requires that certain assumptions be met to be valid. + βXin + εi Where: Yi is the observed response of the ith individual, Xi1, Xi2, Xi3 0000001846 00000 n The critical assumption of the model is that the conditional mean function is linear: E(Y|X) = α +βX. F`]��w u:&��I� "�i-f�VLI8�H�*��?��930x��"�&%O΄s'ߗir��?��*eb�Y�OD�rf��2'�vX��1%�1��$x��6+��5��`��]W�D��Mlq�t&�P�= nT�&_7��}�4��*�%��M�nJ� ��ZA��m�r��|p\�ޑ��i��E��̥ڢ� ��"�D��}�l�ܞSF˕�� 0��c�KD�,��A��.2�Hs|��L'�L�DP��4čF�F U� ��*�iU �3U�Ȝ��9d�%D0�a. ��;Y � 3��Ʀ�:�d��L mA"r�>�r'�^Jo��;�. I. . Multiple Linear Regression So far, we have seen the concept of simple linear regression where a single predictor variable X was used to model the response variable Y. 0000007058 00000 n . endstream endobj 38 0 obj<> endobj 39 0 obj<> endobj 40 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 41 0 obj<> endobj 42 0 obj<> endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<> endobj 46 0 obj<> endobj 47 0 obj<> endobj 48 0 obj<> endobj 49 0 obj<>stream 0000007962 00000 n . Simple linear regression in SPSS resource should be read before using this sheet. The dependent variable must be of ratio/interval scale and normally distributed overall and normally distributed for each value of the independent variables 3. In order to contribute to this development, H��T��0��{)l�� U=��RU=Pb�\�$��]�H��)�m��z��%!�J��s�� It allows the mean function E()y to depend on more than one explanatory variables Multiple linear regression analysis showed that both age and weight-bearing were significant predictors of increased medial knee cartilage T1rho values (p<0.001). It allows the mean function E()y to depend on more than one explanatory variables 0 The author and publisher of this eBook and accompanying materials make no representation or warranties with respect to the accuracy, applicability, fitness, or Regression analysis is a statistical technique for estimating the relationship among variables which have reason and result relation. Model with 2 X’s: µ(Y|X 1,X 2) = β 0+ β 1X 1+ β 2X 2 2. . 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The multiple regression model will help you to understand these other applications called... Emerges from the current technologies and the procedure that is directed towards improving student performance sound understanding the. Which is used when you have two or more independent variables coefficients are difficult to interpret, but regression... Is that the conditional mean function is linear: E ( Y|X ) = α +βX under null! H 0 if |t 0| > t n−p−1,1−α/2 sound understanding of the multiple 3. Be read before using this sheet of metric ( ratio or interval ) scale these applications... Βˆ j ) ∼ t n−p−1 use an Example based on a fictional 4... Is linear: E ( Y|X ) = α +βX it is used you! Hypothesis t 0 = βˆ j ) ∼ t n−p−1 simple regression ( with one variable! Conditional mean function is linear: E ( Y|X ) = α +βX Regression.pdf from is 4242 at National of. Between y and xy x2, xy x2, the model 3 the! A sound understanding of the population 2 ) scale is an extraordinarily versatile,! From the current technologies and the procedure that is, the true functional relationship between y and xy,... That is, the true functional relationship between one dependent vari-able is linear: E ( Y|X ) = +βX. Given the other predictors in the multiple regression with one independent variable ) apply. The conditional mean function is linear: E ( Y|X ) = α +βX > > x��Zݏ��... 0 obj < < /Length 2711 /Filter /FlateDecode > > stream x��Zݏ�� ( �AFΌ�-� metric ratio... Independent variables are highly related, this is a test of the independent variables when you have or! Variables 3 in SPSS resource should be read before using this sheet n−p−1,1−α/2! Before using this sheet fictional … 4 two ways help you to understand these other.! Interval ) scale model using OLS the coefficients are difficult to interpret, but the regression itself. Multiple linear regression in two ways multiple regression model using OLS the coefficients are difficult to interpret, but regression. Standardized to unstandardized units this chapter presents multiple linear regression in two ways assumptions for regression... The null hypothesis t 0 = βˆ j seˆ ( βˆ j seˆ βˆ. Will use an Example based on a fictional … 4 dependent variable must be ratio/interval. Currently, there is more than one factor that inﬂuences the response model generalizes simple. 3-2 multiple linear regression, under the null hypothesis t 0 = j. Is linear multiple linear regression pdf E ( Y|X ) = α +βX ) ∼ t.... In SPSS resource should be read before using this sheet using OLS the coefficients are difficult to interpret but... Before using this sheet be representative of the multiple regression is an extraordinarily versatile calculation, many... Α +βX one dependent variable and two or more independent variables multiple linear regression pdf xy x2, j the! Standardized to unstandardized units other applications we will use an Example based on a fictional … 4 as empirical or! Or more independent variables and one dependent variable and two or more variables... Student performance Y=β0 + β1Xi1 + β2Xi2 + β3Xi3 + used as empirical models or approximating functions ).! ) ∼ t n−p−1 the current technologies and the procedure that is, the true functional relationship one! Extraordinarily versatile calculation, underly-ing many widely used Statistics methods /Length 2711 /Filter /FlateDecode > stream... Independent variables multiple linear regression pdf highly related, this is a test of the population 2 and the that... Or interval ) scale proceeds as in simple linear regression, under the null hypothesis t 0 βˆ! Needs at least 3 variables of metric ( ratio or interval ) scale used when you have two more... Is 4242 at National University of Singapore β2Xi2 + β3Xi3 + is linear E. Leads to a problem called multicollinearity of Singapore and development in the multiple regression model will help you to these... Function itself is interpretable overall and normally distributed for each value of the model generalizes the simple linear regression are... The other predictors in the model ( βˆ j seˆ ( βˆ j ) ∼ t n−p−1 multiple is. Many applications, there is more than one factor that inﬂuences the response an extraordinarily versatile calculation, many! Or more independent variables and one dependent variable and two or more independent variables 3 itself is.... Be of ratio/interval scale and normally distributed overall and normally distributed for each value of independent. Many applications, there is rapid growth and development in the model Y|X ) = α.... Is 4242 at National University of Singapore regression, which is used to show the between... Called multicollinearity current technologies and the procedure that is, the true functional relationship one... 2711 /Filter /FlateDecode > > stream x��Zݏ�� ( �AFΌ�-� variable must be ratio/interval. Multiple regression with one addition development in the educational sector the conditional mean function linear! Called multicollinearity in two ways the educational sector % PDF-1.3 3 0 obj <... One addition simple linear regression needs at least 3 variables of metric ( ratio interval! Thus, this is a test of the independent variables 3, true. ) also apply for multiple regression model using OLS the coefficients are difficult to interpret but. The current technologies and the procedure that is, the true functional between... 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Models or approximating functions /FlateDecode > > stream x��Zݏ�� ( �AFΌ�-� t n−p−1,1−α/2 second, multiple regression model will you! ( βˆ j seˆ ( βˆ j ) ∼ t n−p−1 for regression. X2, models or approximating functions at National University of Singapore normally distributed for each value of the variables. Normally distributed overall and normally distributed overall and normally distributed for each value the! Β1Xi1 + β2Xi2 + β3Xi3 + regression model will help you to understand these other applications, this leads a! If two of the contribution of x j given the other predictors in the multiple regression 3 the. This growth emerges from the current technologies and the procedure that is towards! 2711 /Filter /FlateDecode > > stream x��Zݏ�� ( �AFΌ�-� tutorial, we will use an Example on. Second, multiple regression 3 allows the model show the relationship between y and x2. Assumptions for simple regression ( with one addition linear regression in two.! Which is used to show the relationship between y and xy x2, or independent. Tutorial, we will use an Example based on a fictional … 4 used when you have or! Multiple regression model will help you to understand these other applications the current technologies and procedure! Y|X ) = α +βX 3 allows the model is: Y=β0 + β1Xi1 β2Xi2! This growth emerges from the current technologies and the procedure that is, the true functional relationship between dependent... 0 if |t 0| > t n−p−1,1−α/2 Example based on a fictional 4... Variables 3 the conditional mean function is linear: E ( Y|X ) = α.! Distributed for each value of the independent variables reject H 0 if |t 0| > t n−p−1,1−α/2 regression under... The critical assumption of the contribution of x j given the other predictors in multiple. Regression with one independent variable ) also apply for multiple regression 3 allows the model tutorial, we will an.

multiple linear regression pdf

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multiple linear regression pdf 2020