Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    Two questions of my assignment:

    I have attached the calculations... However, what's the interpretation of these? :/
    Offline

    13
    ReputationRep:
    (Original post by SikoSiko)
    I have attached the calculations... However, what's the interpretation of these? :/
    Attachment missing...
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Gregorius)
    Attachment missing...
    Here you go!
    Offline

    13
    ReputationRep:
    (Original post by SikoSiko)
    Two questions of my assignment:

    1. "Is the average salary different for persons with different categories of education?"
    2. "Are the conclusions from the previous question changed if gender is included in the analysis?"

    I have attached the calculations... However, what's the interpretation of these? :/
    Taking question 1 first, then answer is "yes". The p-value attached to the F-statistic in the Analysis of variance table is very small. This is the p-value assciated with the covariate that represents the category of schooling. If you then look at the parameter estimates, you can see a monotonic increasing value of the average salary as the level of education increases. Also note that the value of Adjusted R^2 is small (around the 10% mark), so the level of education explains only a little bit of the overall variation in salary levels.

    For question 2, the answer is still "yes" but the details are more complex. Can you take the answer I gave you for the first part and see why I make these conclusions?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Gregorius)
    Taking question 1 first, then answer is "yes". The p-value attached to the F-statistic in the Analysis of variance table is very small. This is the p-value assciated with the covariate that represents the category of schooling. If you then look at the parameter estimates, you can see a monotonic increasing value of the average salary as the level of education increases. Also note that the value of Adjusted R^2 is small (around the 10% mark), so the level of education explains only a little bit of the overall variation in salary levels.

    For question 2, the answer is still "yes" but the details are more complex. Can you take the answer I gave you for the first part and see why I make these conclusions?
    I think so... Because the AdjR^2 is only about the 10% wouldn't that make the difference insignificant?
    Offline

    13
    ReputationRep:
    (Original post by SikoSiko)
    I think so... Because the AdjR^2 is only about the 10% wouldn't that make the difference insignificant?
    Adjusted R^2 is around 20% in the second analysis. Roughly speaking, this means that adding the sex variable is doubling the amount of explanatory information.

    However, take a look at the estimates of the mean effects of the education categories (that appear to be given relative to the top category).
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Gregorius)
    Adjusted R^2 is around 20% in the second analysis. Roughly speaking, this means that adding the sex variable is doubling the amount of explanatory information.

    However, take a look at the estimates of the mean effects of the education categories (that appear to be given relative to the top category).
    There is something I don't understand...
    Offline

    13
    ReputationRep:
    (Original post by SikoSiko)
    There is something I don't understand ... In question 2 I'm asked whether the conclusion changes if I include gender... So it does change because the AdjR is is greater... But it seems that salary and education level are still more "linked" than salary and gender.
    Is it that gender affects the salary, but that education is the variable that "affects" salary the most?
    Given that adjusted R^2 is around 10% for the first model and 20% for the second, it looks as though they each have roughly the same explanatory power.

    Now, I don't recognize the programme output (whcih programme is it?) and it looks as though the second analysis only has four degrees of freedom, which suggests that the model is not fitting the interaction term between gender and education. Also, the slight problem with model fit suggests that the interaction is missing. So this doesn't look like a standard two-way AoV. Can you force it to fit the interaction?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Gregorius)
    Given that adjusted R^2 is around 10% for the first model and 20% for the second, it looks as though they each have roughly the same explanatory power.

    Now, I don't recognize the programme output (whcih programme is it?) and it looks as though the second analysis only has four degrees of freedom, which suggests that the model is not fitting the interaction term between gender and education. Also, the slight problem with model fit suggests that the interaction is missing. So this doesn't look like a standard two-way AoV. Can you force it to fit the interaction?
    Yes, just a moment!!
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Gregorius)
    Given that adjusted R^2 is around 10% for the first model and 20% for the second, it looks as though they each have roughly the same explanatory power.

    Now, I don't recognize the programme output (whcih programme is it?) and it looks as though the second analysis only has four degrees of freedom, which suggests that the model is not fitting the interaction term between gender and education. Also, the slight problem with model fit suggests that the interaction is missing. So this doesn't look like a standard two-way AoV. Can you force it to fit the interaction?
    Perhaps this is what you mean?
    Offline

    13
    ReputationRep:
    (Original post by SikoSiko)
    Perhaps this is what you mean?
    OK, so the interaction term just crawls into the category of being interesting; doesn't improve the adjusted R^2 by much, though. So, using this model, look at the average effects in the different age by sex categories.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.