LO 3.2.1.B
Learning Objective: Â Calculate the value of RSS.
Review:
- Residual sum squares (RSS)
![<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>S</mi><mi>S</mi><mo>=</mo><mo> </mo><mstyle displaystyle="false"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover></mstyle><msubsup><mi>e</mi><mi>i</mi><mn>2</mn></msubsup><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mfenced open="[" close="]"><mrow><msub><mi>y</mi><mi>i</mi></msub><mo>-</mo><msub><mover><mi>y</mi><mo>^</mo></mover><mi>i</mi></msub></mrow></mfenced><mn>2</mn></msup></math>](https://lh7-rt.googleusercontent.com/docsd/ANYlcfCwEKgXqkM78FtjVGfoO4FhvVsV66MGiCIFv_watz8OuLbUGo3iCZ-FQSK2uu91Hrj-_UpELtIfgue0YJDonhEyaE29USLN9VIn8jx0mPQFB80GvATsklzaV4jnSq9sU_hb5wDRHbeXhFpYYZrEBXsZcGbANbAAkw "R S S equals space begin inline style sum from i equals 1 to n of end style e subscript i superscript 2 equals sum from i equals 1 to n of open square brackets y subscript i minus y with hat on top subscript i close square brackets squared")
![<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>S</mi><mi>S</mi><mo>=</mo><msup><mfenced open="[" close="]"><mrow><mo> </mo><msub><mi>y</mi><mn>1</mn></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>0</mn></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>1</mn></msub><msub><mi>x</mi><mn>1</mn></msub></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced open="[" close="]"><mrow><mo> </mo><msub><mi>y</mi><mn>2</mn></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>0</mn></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>1</mn></msub><msub><mi>x</mi><mn>2</mn></msub></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msup><mfenced open="[" close="]"><mrow><mo> </mo><msub><mi>y</mi><mi>n</mi></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>0</mn></msub><mo>-</mo><msub><mover><mi>β</mi><mo>^</mo></mover><mn>1</mn></msub><msub><mi>x</mi><mi>n</mi></msub></mrow></mfenced><mn>2</mn></msup></math>](https://lh7-rt.googleusercontent.com/docsd/ANYlcfDzutxm4OsnwrGJW6H4Hjl9YzmECSZ5Rbh8Lr9UzBTmj7R-KgJN54IJN6arbpKlj0g1vspLdhUjh_eCp-SCoqkwqueZokkWDtDtTMXcDb1yrbEzYt6NPxrfBQqqZ-o38hKHCKojZf6evkSEyfNijHS6PpG-A9mklg "R S S equals open square brackets space y subscript 1 minus beta with hat on top subscript 0 minus beta with hat on top subscript 1 x subscript 1 close square brackets squared plus open square brackets space y subscript 2 minus beta with hat on top subscript 0 minus beta with hat on top subscript 1 x subscript 2 close square brackets squared plus..... plus open square brackets space y subscript n minus beta with hat on top subscript 0 minus beta with hat on top subscript 1 x subscript n close square brackets squared")
        where
 
 and 
 are the estimates of the parameters/coefficients of the regression.
LO 3.2.1.B
Learning Objective: Â Calculate the value of RSS.
Review:
        where
  and  are the estimates of the parameters/coefficients of the regression.