Multiple Regression Analysis

If y is a dependent variable (aka the response variable) and x1, …, xk are independent variables (aka predictor variables), then the multiple regression model provides a prediction of y from the xi of the form

General multiple regression model


36 Responses to Multiple Regression Analysis

  1. Neetu sharma says:

    very knowledgable article.

  2. Michael says:

    Very useful and practical. Actually the section for coefficient analisys is sustantive.

  3. Tapan kumar mahanta says:

    Sir i am unable to get the result by applying the command =TREND(B4:B53,C4:E53,G6:I8) at figure 2 of multiple regression analysis.
    please inform me how i will over come the problem and i will get the same result what you got at table 2.

    • Charles says:

      TREND is an array formula. It is essential that you press Ctrl-Shift-Enter (and not just Enter) after inserting the formula. If this is not the problem, let me know.

  4. Tapan kumar mahanta says:

    i am doing the same Ctrl-Shift-Enter but the result is not coming. final result is coming like this #Value.
    for my problem Y= b0+b1x1 +b2x2 +b3x3 +b4x4 +b5x5 +b6x6
    Y matrix=(22*1)
    x matrix=(x1 x2 x3 x4 x5 x6)
    x1….x6 matrix=(22*6)
    please tell how i can solve this problem using multiple regression. using TREND and LINSET command.

  5. umesh patil india says:

    Compressive Strength Tensile Strength % polymer added
    25.33 2.44 0
    28 2.69 1
    33.63 3.11 2
    34.52 3.3 3
    32.74 3.06 4
    28.89 2.78 5
    25.93 2.55 6
    24 2.12 7
    21.62 1.93 8
    thirdt column values are independent and remaining 2 columns r dedenedent how 2 do multiple regression? plz

    • Charles says:

      The usual multiple regression model would have two independent variables and one dependent variable. Since you have two dependent variables and one independent, you can create two separate regression models with one dependent and one independent variable. If you want a single regression model with two dependent variables then you probably want multivariate regression. R provides this capability.

  6. just a guy says:

    According to this formula
    Poverty = 0.457 + .00142 ∙ Infant Mortality + .0363 ∙ White + 1.279 ∙ Crime

    for a certain case of Alabama where Infant Mortality =9, White= 71 and Crime= 448
    Poverty should be 0.457 + 0.01278 + 2.577 + 573 = 573

    And not around 15.7 as it is in the table. The result is clearly off and contribution from Crime is significantly higher then contribution from first 2 factors. This would make sense if first 2 factors do not correlate at all with Poverty but i think this is not the case.

    I might be wrong but it appears to me that something is a bit off…

    • Charles says:

      You are correct. I made two typing mistakes when I copied the coefficients in Figure 3. The correct regression line should be:

      Poverty (predicted) = 0.437 + 1.279 ∙ Infant Mortality + .0363 ∙ White + 0.00142 ∙ Crime

      Thanks for catching this error.


  7. Niel says:

    Hello Mr. Zaiontz,
    I am conducting a study with 4 independent variables and one dependent variables. These 4 independent variables include 3 survey data and the other one is method of teaching. The dependent var is grade. Can I use multiple regression? How am I going to come up with a regression model? Please help me…. thanks

  8. student says:

    Hi! I am doing my research using likert scale (effect of attitudes) as dependent variable to english performance( ind. var). What stat tool would I employ? thanks

    • Charles says:

      It really depends on what you are trying to demonstrate. What hypothesis are you tryin to test? It is not sufficient to say how many variables you have.

  9. student says:

    3 dependent vars (surveys) and one independent var (performance)

  10. SURESH NAIR says:

    Dear Sir
    I’m preparing budget for my company (production & sales budget) for different products. I had data of 3 years of production & sales for different product. Can you please help me for future projection which statistical formula will be helpful


    • Charles says:

      Depending on what the data looks like multiple regression might be a way to make the projection. When you say that you have 3 years, does that means that you have three data elements for production & sales for each product? Or do you have monthly or weekly data for the 3 years? I ask since with only 3 data elements, projections will be somewhat limited.

  11. Jai says:

    Dear all,
    I am Jai, I am using this regression analysis for Weibull calculation, but I am looking for some kind of procedure, by which the regression analysis will update automatically. Because currently if I change the input data, then only graph is changing (other calculations are not changing, so if I change the data then I have to run regression analysis once again)
    I would really appriciate, if someone can provide me the details about autoupdation of Regression Analysis.


    • Charles says:


      The analysis performed by Excel’s Regression data analysis tool does not update automatically when the input data is changed.
      The Regression data analysis tool provided by the Real Statistics Resource Pack will update automatically when the data is changed. It also handles 64 independent variables (instead of only 16 variables supported by the standard Excel Regression tool).

      You can download the Real Statistics Resource Pack for free by going to the webpage Please make sure that you install the software as described on that webpage.

      See webpage for more information about how to use the Real Statistics Regression data analysis tool.


      • Charu says:

        Dear Sir,

        I need to carry out multiple regression analysis on ordinal (satisfaction measures) independent variables. There are three parameters each categorised into factors and subfactors (variables). Each subfactor includes multiple questions to get satisfaction rating. Thus summing up the scores from questions to subfactors; subfactors to factors; factors to each respective paramater and finally combined score of all three parameters considered as score of the aspect of interest. My first question is whether the method is correct, and second is which specific regression analysis method should I use. Sample size is 300 households within 16 clusters equally divided into two categories.

        • Charles says:

          The approach seems reasonable from what I understand, but with such little detail I cannot say whether the method is correct or not, nor which type of regression analysis to use.

  12. Jai says:

    Dear Sir,
    thank you very much for your response.
    Now the results of regression analysis are updating as per the changes in the data set.

    but if I change the no. of inputs (like- earlier I have used 50 data points and now if I try the same with 48 data points), then this regression analysis is not showing any results.

    So kindly do the needful to resolve the issue.

    Thank you once again for your support.


  13. Jason says:

    Dear Charles,

    Your Real Statistics Add-In tools are great! Just wondering if there is a way to constrict the constant to zero when using the Linear Regression tool?



    • Charles says:

      At present I don’t provide any way of constricting the constant to zero. I understand that there is no general agreement for how to do this. Excel’s Regression data analysis tool does provide this capability, but I am not sure whether the approach used is widely accepted.

  14. Alicia says:

    Dear Charles,

    I am investigating the dependency of a set of PCA components (each component with 27 values, that would be my dependent variables) with regard to a set of design evaluations (12 values, independent variables), I would like to ask you which is the best regression method for datasets which don’t have the same dimension?

    Many thanks in advance

    • Charles says:

      I don’t completely understand your question. Regression is normally performed on one dataset and so I don’t know how to intend to use multiple datasets, unless you you are simply referring to the data for each variable as a different dataset. In this case, perhaps by different dimensions you mean that some data is missing which is causing the sample sizes to be different. Please clarify these points.

  15. sadia sadi says:

    sir i am un able to aply the regression on 1 dependent and 3 independent variabls plz help me

    • Charles says:

      Are you trying to do the reression usin the standard Excel Regression data analysis tool or are you using the Real Statistics Linear Regression data analysis tool or something else?

  16. mae says:

    Please,who can help me among you here guys in doing the stat of my research. it’s really nerve cracking for because i’m not really good in stat.E mail me please,I would really appreciate your help. =(

  17. David Crownover says:

    I’m doing a multiple regression on 23 independent variables. Granted, many of them are interaction variables. The 23rd variable is not giving any coefficients nor standard error data, which is then causing errors in the following cells. I’ve tried running it again without the 23rd variable and the 22nd variable is fine, but when I add in the 23rd, it doesn’t work. Any thoughts?

    • Charles says:

      A possible explanation is collinearity (see Collinearity), but I’d have to see the data to figure out what the problem is. Presumably you are using the Real Statistics data analysis tool since the Excel Regression tool is limited to 16 independent variables.

      • David Crownover says:

        I am using that and thank you for that tool. I’m pretty confident that it is Collinearity as the variable is actualy interacted between 3 other variables and one is a squared variable. (X2sqX3X4) but there are other collinear variables in the entire data set so I was surprised when it was the only one that did that.

  18. Dear Sir,
    What stat formula will I use if I have one independent variable (personal formation program of the school) and 3 dependent variables (behavior at home, in school and in the community? You may email me for the answer. Thanks.

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