intercept in linear regression
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hi all,
I have a question: I'm running a linear regression and have the entries below for the x independent variable: 4032 3680 1317 869 510 249 0 and the respective entries for the y, the dependent variable as follows: .69897 .69897 .95424 1.07918 1.04139 1.04139 1.07918 The intercept should be the last value for y, as this is where the regression line meets the y-axis. However, when I run the regression and look at the intercept in the Results output the intercept is 1.09636, instead of 1.07918. I.e. this is what I get from a simple linear regression with y dependent, x independent: Coefficients(a)(,)(b) Unstan/zed Coef Stand/zed Coeff Model B Std. Error Beta t Sig. 1 (Constant) 1.096 .020 54.902 .000 x .000 .000 -.980 -10.966 .000 Can anyone enlighten me as to why that would be? Thank you |
Re: intercept in linear regression
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Your last data point is x = 0 and y = 1.07918. However, the regression line does not necessarily go through a specific data point. It does go through the mean on x and the mean on y.
wbw William B. Ware, Ph.D. McMichael Professor of Education 2011-2013 Educational Psychology, Measurement, and Evaluation CB #3500 - 118 Peabody Hall University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3500 Office: (919)-962-2511 Fax: (919)-962-1533 Office: 118 Peabody Hall EMAIL: [hidden email] <mailto:[hidden email]> Adjunct Professor, School of Social Work Academy of Distinguished Teaching Scholars at UNC-Chapel Hill -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of xenia Sent: Monday, January 28, 2013 8:07 AM To: [hidden email] Subject: intercept in linear regression hi all, I have a question: I'm running a linear regression and have the entries below for the x independent variable: 4032 3680 1317 869 510 249 0 and the respective entries for the y, the dependent variable as follows: .69897 .69897 .95424 1.07918 1.04139 1.04139 1.07918 The intercept should be the last value for y, as this is where the regression line meets the y-axis. However, when I run the regression and look at the intercept in the Results output the intercept is 1.09636, instead of 1.07918. I.e. this is what I get from a simple linear regression with y dependent, x independent: Coefficients(a)(,)(b) Unstan/zed Coef Stand/zed Coeff Model B Std. Error Beta t Sig. 1 (Constant) 1.096 .020 54.902 .000 x .000 .000 -.980 -10.966 .000 Can anyone enlighten me as to why that would be? Thank you -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/intercept-in-linear-regression-tp5717749.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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In reply to this post by xenia
Hi Xenia,
The simple answer is that the intercept will not be the value of a data point when X=0. The regression line represents predicted values, not actual values. You can think of the regression as giving the expected value: the intecept is an estimate of the mean value when X=0, but you would expect some variablitiy about the mean. You observed value at X=0 can be thought of as a sample which happened to be a bit below the (predicted) mean. Similarly, your observed value when x=869 (1.07918) is slightly higher than the predicted mean. -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of xenia Sent: 28 January 2013 13:07 To: [hidden email] Subject: intercept in linear regression hi all, I have a question: I'm running a linear regression and have the entries below for the x independent variable: 4032 3680 1317 869 510 249 0 and the respective entries for the y, the dependent variable as follows: .69897 .69897 .95424 1.07918 1.04139 1.04139 1.07918 The intercept should be the last value for y, as this is where the regression line meets the y-axis. However, when I run the regression and look at the intercept in the Results output the intercept is 1.09636, instead of 1.07918. I.e. this is what I get from a simple linear regression with y dependent, x independent: Coefficients(a)(,)(b) Unstan/zed Coef Stand/zed Coeff Model B Std. Error Beta t Sig. 1 (Constant) 1.096 .020 54.902 .000 x .000 .000 -.980 -10.966 .000 Can anyone enlighten me as to why that would be? Thank you -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/intercept-in-linear-regression-tp5717749.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: intercept in linear regression
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In reply to this post by xenia
scatterplot
your data.
then go to the output file edit the graph and fit a line (linear) GGRAPH /GRAPHDATASET NAME="graphdataset" VARIABLES=VAR00001[LEVEL=SCALE] VAR00002 MISSING=LISTWISE REPORTMISSING=NO /GRAPHSPEC SOURCE=INLINE. BEGIN GPL SOURCE: s=userSource(id("graphdataset")) DATA: VAR00001=col(source(s), name("VAR00001")) DATA: VAR00002=col(source(s), name("VAR00002")) GUIDE: axis(dim(1), label("VAR00001")) GUIDE: axis(dim(2), label("VAR00002")) ELEMENT: point(position(VAR00001*VAR00002)) END GPL. Art Kendall Social Research ConsultantsOn 1/28/2013 8:06 AM, xenia wrote:
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants |
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How does that answer my question?
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In reply to this post by MOram
Thank you for this, I also found that if one goes to the Regression algorithms in SPSS help , there is a formula given for the calculation of the intercept:On 28 January 2013 13:53, Michael Oram [via SPSSX Discussion] <[hidden email]> wrote:
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Re: intercept in linear regression
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In reply to this post by xenia
eyeball
where the line hits the y axis
Art Kendall Social Research ConsultantsOn 1/28/2013 9:14 AM, xenia wrote: How does that answer my question? -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/intercept-in-linear-regression-tp5717749p5717753.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Art Kendall
Social Research Consultants |
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