Four regression models are fitted to explore the effect of age on BMI. Use the r

Question

Four regression models are fitted to explore the effect of age on BMI. Use the results (see below) to answer the following questions.

Model 1:
. regress bmi age

      Source |       SS       df       MS              Number of obs =    1285
-------------+-----------------------------           F( 1, 1283) =   27.53
       Model | 565.735749     1 565.735749           Prob > F      = 0.0000
    Residual |   26365.083 1283 20.5495581           R-squared     = 0.0210
-------------+-----------------------------           Adj R-squared = 0.0202
       Total | 26930.8188 1284 20.9741579           Root MSE      = 4.5332

------------------------------------------------------------------------------
         bmi |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+---------------------------------------------------------------
         age | -.0779364   .0148537    -5.25   0.000    -.1070766   -.0487962
       _cons |   32.52028   .9915627    32.80   0.000     30.57502    34.46554
------------------------------------------------------------------------------

Model 2:
. regress bmi gender

      Source |       SS       df       MS              Number of obs =    1285
-------------+-----------------------------           F( 1, 1283) =   11.35
       Model | 236.116065     1 236.116065           Prob > F      = 0.0008
    Residual | 26694.7027 1283 20.8064713           R-squared     = 0.0088
-------------+-----------------------------           Adj R-squared = 0.0080
       Total | 26930.8188 1284 20.9741579           Root MSE      = 4.5614

------------------------------------------------------------------------------
         bmi |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+---------------------------------------------------------------
      gender |   .9167072   .2721242     3.37   0.001       .38285    1.450564
       _cons |   26.73945   .2239109   119.42   0.000     26.30018    27.17872
------------------------------------------------------------------------------

Model 3:
. regress bmi age gender

      Source |       SS       df       MS              Number of obs =    1285
-------------+-----------------------------           F( 2, 1282) =   20.01
       Model | 815.142202     2 407.571101           Prob > F      = 0.0000
    Residual | 26115.6766 1282 20.3710426           R-squared     = 0.0303
-------------+-----------------------------           Adj R-squared = 0.0288
       Total | 26930.8188 1284 20.9741579           Root MSE      = 4.5134

------------------------------------------------------------------------------
         bmi |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+---------------------------------------------------------------
         age | -.0788591   .0147914    -5.33   0.000    -.1078771   -.0498411
      gender |   .9423034   .2693045     3.50   0.000     .4139776    1.470629
       _cons |   31.94339   1.000919    31.91   0.000     29.97977    33.90701
------------------------------------------------------------------------------

Model 4
. regress bmi age gender agegender

      Source |       SS       df       MS              Number of obs =    1285
-------------+-----------------------------           F( 3, 1281) =   15.60
       Model | 949.005478     3 316.335159           Prob > F      = 0.0000
    Residual | 25981.8133 1281   20.282446           R-squared     = 0.0352
-------------+-----------------------------           Adj R-squared = 0.0330
       Total | 26930.8188 1284 20.9741579           Root MSE      = 4.5036

------------------------------------------------------------------------------
         bmi |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+---------------------------------------------------------------
         age | -.0264662   .0251744    -1.05   0.293    -.0758537    .0229213
      gender |   6.219454   2.071637     3.00   0.003      2.15528    10.28363
   agegender | -.0798335   .0310753    -2.57   0.010    -.1407975   -.0188695
       _cons |   28.48597    1.67591    17.00   0.000     25.19814     31.7738
------------------------------------------------------------------------------


(a) Describe the age effect on BMI?

(b) Describe the gender effect on BMI?

(c) Is there a significant interaction effect between age and gender on BMI? If yes, please explain.

(d) From the output, which measure will you use to select a better model? Based on the selected measure, which model will you choose?

(e) How much variation of BMI is explained by the selected model?

Explanation / Answer

Age is significantly predicting BMI, t=-5.25, P =0.000.

The relation is negative, when age increases by 1, BMI decreases by -0.0779

(b) Describe the gender effect on BMI?

gender is significantly predicting BMI, t=3.37, P=0.001

when gender is male(assuming male=1) , BMI increases by 0.9167

(c) Is there a significant interaction effect between age and gender on BMI? If yes, please explain.

interaction effect between age and gender is significant, t= -2.57, P=0.01.

(d) From the output, which measure will you use to select a better model? Based on the selected measure, which model will you choose?

we select adjusted R square.

We select model 4, because this adjusted R square 0.033 is larger than others.

(e) How much variation of BMI is explained by the selected model?

               3.3% variation of BMI is explained by the selected model.

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