Question

Write down the two systematic components corresponding to females and males.

## 
## Call:
## lm(formula = Percent.Fat ~ Age * Gender, data = humanfat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.6756 -2.8862 -0.2464  1.9100  9.1641 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  20.1116     6.2395   3.223  0.00613 **
## Age           0.2401     0.1204   1.994  0.06600 . 
## GenderM     -29.2692    10.4098  -2.812  0.01386 * 
## Age:GenderM   0.5725     0.2893   1.978  0.06790 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.488 on 14 degrees of freedom
## Multiple R-squared:  0.8016, Adjusted R-squared:  0.7591 
## F-statistic: 18.86 on 3 and 14 DF,  p-value: 3.455e-05

Answer 1

Systematic Component - specifies the explanatory variables (X₁, X₂, ... X_k) in the model, more specifically their linear combination in creating the so called linear predictor; e.g., β₀ + β₁x₁ + β₂x₂ as we have seen in a linear regression.

The Systematic component correesponding to female and male is

Female	20.1116+0.2401*Age
Male	-9.1576+0.8126*Age

The detailed solution is given in the attached fie.Hope this helps.