OLS showing unexpected sign

[nonsi nkomo]

Hi

I am running an OLS regression. I am using the dependent variable BMI and the independent variable exercise. Exercise is measured as the number of times a week one exercises for 30 mins or more. I keep getting a positive and insignificant coefficient for exercise even after including more explanatory variables. I have tried to use the log of BMI but the result remains the same. I have also tried removing outliers in the BMI data but i still get a positive coefficient. Please help =(

Kind Regards
Nonsi Nkomo

[Nick Cox]

Show us a scatter plot

scatter BMI exercise

[nonsi nkomo]

This is the graph before removing any outliers or taking the log of BMI

[Carlo Lazzaro]

Nonsi:
have you checked for omitted variable bias (-estat ovtest-)?
Sharing what you typed and what Stats gave you back (via CODE delimiters, please) would help as well.

[nonsi nkomo]

Hi Carlo

Here is the code I used.

reg DBMI8 W8EXERCISE

      Source |       SS           df       MS      Number of obs   =     7,069
-------------+----------------------------------   F(1, 7067)      =      0.55
       Model |  17.9850806         1  17.9850806   Prob > F        =    0.4597
    Residual |  232536.932     7,067  32.9046175   R-squared       =    0.0001
-------------+----------------------------------   Adj R-squared   =   -0.0001
       Total |  232554.917     7,068  32.9025066   Root MSE        =    5.7363

------------------------------------------------------------------------------
       DBMI8 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  W8EXERCISE |   .0237712   .0321532     0.74   0.460    -.0392586    .0868011
       _cons |   25.18001   .1181194   213.17   0.000     24.94846    25.41156
------------------------------------------------------------------------------

.

Kind Regards
Nonsi Nkomo

[nonsi nkomo]

Hi Carlo

I have now performed the omitted variable bias test and my results are as follows.

estat ovtest

Ramsey RESET test using powers of the fitted values of DBMI8
       Ho:  model has no omitted variables
                F(3, 7064) =      0.22
                  Prob > F =      0.8807

Kind Regards
Nonsi Nkomo

[Rich Goldstein]

two things that may help:

1. ratio variables should be avoided; you might want to see the citations in #2 and #3 in https://www.statalist.org/forums/for...y-zit-on-zit-1

2. on the "wrong" sign, you might want to see the various discussions, including citations, in https://www.statalist.org/forums/for...ols-regression

[Joseph Coveney]

I don't understand why you're dumbfounded. You have horribly noisy and improbable data, some not insubstantial proportion of which appears to arise from pulling the interviewer's leg. (I mean, c'mon, someone with a body mass index of 110 exercising four days a week for 30+ minutes each time? That person can scarcely move at all.)

Mixed in with all of the joshing you might have a subpopulation of athletic types whose muscle mass is reflected in relatively higher BMIs who exercise regularly (hence I think the question above about omitted variables), pulling up a plot containing an otherwise overweight sedentary crowd for a net zero slope.

And, amid all of the measurement error, the zero slope is just what you got—it couldn't eke out an estimate (0.02 ± 0.03) coming anywhere near a statistically significant difference from zero despite a sample of over seven thousand. With a random subsample, maybe jittering and smaller symbols so that there isn't so much overlap, you could undoubtedly see the same thing in the scatter plot.

[Nick Cox]

I'd want something more like a box plot for each predictor value. My guess is that each conditional distribution is highly skewed.

[nonsi nkomo]

Hi Joseph

Thank you for the help. I constructed the scatter plot before removing any outliers. Even after removing the outliers in BMI I am still getting a positive coefficient for exercise. I kept 12.75<BMI<36.4. Also I am quite the amateur when it comes to STATA and modelling so I am confused by a lot of the jargon.

Kind Regards
Nonsi Nkomo

[Carlo Lazzaro]

Nonsi:
the situatiion you're experiencing seems similar to the following one:

. regress price rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(1, 67)        =      0.00
       Model |  24770.7652         1  24770.7652   Prob > F        =    0.9574
    Residual |   576772188        67  8608540.12   R-squared       =    0.0000
-------------+----------------------------------   Adj R-squared   =   -0.0149
       Total |   576796959        68  8482308.22   Root MSE        =      2934

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       rep78 |   19.28012   359.4221     0.05   0.957    -698.1295    736.6897
       _cons |   6080.379    1274.06     4.77   0.000     3537.345    8623.413
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of price
       Ho:  model has no omitted variables
                  F(3, 64) =      0.31
                  Prob > F =      0.8160

. predict fitted, xb
(5 missing values generated)

. g sq_fitted=fitted^2
(5 missing values generated)

. regress price rep78 sq_fitted

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(2, 66)        =      0.38
       Model |  6642599.02         2  3321299.51   Prob > F        =    0.6823
    Residual |   570154360        66  8638702.42   R-squared       =    0.0115
-------------+----------------------------------   Adj R-squared   =   -0.0184
       Total |   576796959        68  8482308.22   Root MSE        =    2939.2

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       rep78 |   158316.9   180859.7     0.88   0.385    -202781.1    519414.9
   sq_fitted |  -.6679995   .7632075    -0.88   0.385    -2.191792    .8557935
       _cons |   2.47e+07   2.82e+07     0.88   0.384    -3.16e+07    8.10e+07
------------------------------------------------------------------------------

Despite a non-significant -estat ovtest- (as also proved by the augmented regression with -sq_fitted, that turns out to be non-significant), the R-sq of the original OLS is totally negligible.
I would say that, despite -estat ovtest- outcome passes the muster, my model specification is highly unsatisfactory.

[nonsi nkomo]

Thank you Carlo for the help. Do you think it has something to do with my independent variable, exercise?

[Carlo Lazzaro]

Nonsi:
it may be so; unfortunately, my limited knowledge of your research field does not allow me to reply more positively.

[nonsi nkomo]

Thank you Carlo for the help.

[nonsi nkomo]

Hi Nick

Here is a box plot of the predictor variable exercise.

Kind Regards
Nonsi Nkomo