Comparing these two R outputs, answer the follow question

A study utilized a one-time questionnaire to collect data from 600 people to identify factors associated with body mass index (BMI). The variables for the analysis are described in the table below.

Variable Name	Variable Description	Value
ID	Participant ID	1 to 600
age	Age (in years)	Continuous
sex	Sex assigned at birth	1=Females 0=Males
smoke	Current smoking status	1=Yes 0=No
bmi	Body mass index (kg/m2)	Continuous

To test the association between sex and BMI, the investigators first conducted the following analysis:

> summary(lm(bmi~sex))

Call:

lm(formula = bmi ~ sex)

Residuals:

Min 1Q Median 3Q Max

-11.4563 -2.9997 -0.5004 2.1966 17.8870

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 28.7663 0.2219 129.637 < 2e-16 ***

sex -1.2278 0.4085 -3.005 0.00276 **

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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.564 on 598 degrees of freedom

Multiple R-squared: 0.01488, Adjusted R-squared: 0.01323

F-statistic: 9.032 on 1 and 598 DF, p-value: 0.002764

Is there a statistically significant relationship between sex and BMI based on the above analysis? State your conclusion, and briefly justify your response using the R output.

Next, the investigators performed this second analysis:

> summary(lm(bmi~sex+smoke+age))

Call:

lm(formula = bmi ~ sex + smoke + age)

Residuals:

Min 1Q Median 3Q Max

-10.1280 -2.9205 -0.4545 2.3458 17.5262

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 31.53865 1.46909 21.468 <2e-16 ***

sex -1.04099 0.41222 -2.525 0.0118 *

smoke -1.32750 0.51584 -2.573 0.0103 *

age -0.03989 0.02211 -1.804 0.0717 .

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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.542 on 596 degrees of freedom

Multiple R-squared: 0.02771, Adjusted R-squared: 0.02282

F-statistic: 5.662 on 3 and 596 DF, p-value: 0.0007911

Based on these analyses, was there evidence that the association between BMI and sex was jointly confounded by smoking status and age? Show your work, and briefly justify your response.