If there are three independent variables $x _ { 1 } , x _ { 2 }$, and $x _ { 3 }$ available, then the value of $R ^ { 2 }$ for a multiple regression of $y$ using $x _ { 1 } , x _ { 2 }$, and $x _ { 3 }$ will always be smaller than the value of $r ^ { 2 }$ for a multiple regression of $y$ using just $x _ { 1 }$.

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The Answer of If there are three independent variables $x _ { 1 } , x _ { 2 }$, and $x _ { 3 }$ available, then the value of $R ^ { 2 }$ for a multiple regression of $y$ using $x _ { 1 } , x _ { 2 }$, and $x _ { 3 }$ will always be smaller than the value of $r ^ { 2 }$ for a multiple regression of $y$ using just $x _ { 1 }$.

If There Are Three Independent Variables x1,x2x _ { 1 } , x _ { 2 }x1​,x2​

If There Are Three Independent Variables $x _ { 1 } , x _ { 2 }$