Solution Found!
Ch 11 - 1E
Chapter 11, Problem 1E(choose chapter or problem)
If \(\beta_{0}\) and \(\beta_{1}\) are the least-squares estimates for the intercept and slope in a simple linear regression model, show that the least-squares equation \(\tilde{y}=\widehat{\beta_{0}}+\widehat{\beta_{1} x}\) always goes through the point \((\bar{x}, \bar{y})\). [Hint: Substitute for x in the least-squares equation and use the fact that \(\overline{\beta_{0}}=\bar{y}-\overline{\beta_{1}} \bar{x}\).]
Equation transcription:
Text transcription:
\beta_{0}
\beta_{1}
\tilde{y}=\widehat{\beta{0}}+\widehat{\beta{1} x}
\overline{\beta{0}}=\bar{y}-\overline{\beta{1}} \bar{x}
(\bar{x}, \bar{y})
Questions & Answers
QUESTION:
If \(\beta_{0}\) and \(\beta_{1}\) are the least-squares estimates for the intercept and slope in a simple linear regression model, show that the least-squares equation \(\tilde{y}=\widehat{\beta_{0}}+\widehat{\beta_{1} x}\) always goes through the point \((\bar{x}, \bar{y})\). [Hint: Substitute for x in the least-squares equation and use the fact that \(\overline{\beta_{0}}=\bar{y}-\overline{\beta_{1}} \bar{x}\).]
Equation transcription:
Text transcription:
\beta_{0}
\beta_{1}
\tilde{y}=\widehat{\beta{0}}+\widehat{\beta{1} x}
\overline{\beta{0}}=\bar{y}-\overline{\beta{1}} \bar{x}
(\bar{x}, \bar{y})
ANSWER:Step 1 of 3
we have that
