4.6 ­ Linear Regression and Median Fit Lines Wednesday, November 9, 2016 Students write equations of best­fit lines using linear regression, and write equations of median fit lines. 1 4.6 ­ Linear Regression and Median Fit Lines Homework. 2 4.6 ­ Linear Regression and Median Fit Lines 3 4.6 ­ Linear Regression and Median Fit Lines 4.1 Vocab. Slope ­ Intercept Form ­ An equation in the form y = mx + b Constant Functions ­ Written in slope intercept form as y = 0x + b, or y = b 4.3 Vocab. Point ­ Slope Form ­ An equation in the form y ­ y1 = m(x­x1) 4 4.6 ­ Linear Regression and Median Fit Lines Best­Fit Line ­ A very precise line of fit. Linear Regression ­ A complex algorithm that calculates the best­fit line. Correlation Coefficient ­ This number, r, tells you if the correlation is positive or negative and how closely the best fit line models the data. The number, r, is always between ­1 and 1. 5 4.6 ­ Linear Regression and Median Fit Lines 6 4.6 ­ Linear Regression and Median Fit Lines Correlation Coefficient, r If r is greater than zero and less than or equal to 1. We have a positive correlation. The closer it is to 1, the stronger the positive association is. If r is greater than or equal to ­1 and less than 0. We have a negative correlation. The closer we get to ­1, the stronger the negative correlation is. 7 4.6 ­ Linear Regression and Median Fit Lines Regression Line: y = .23206x + ­456.032 Correlation Coefficient: .875515 8 4.6 ­ Linear Regression and Median Fit Lines 9 4.6 ­ Linear Regression and Median Fit Lines Regression Line: Correlation Coefficient: 10 4.6 ­ Linear Regression and Median Fit Lines Regression Line: Correlation Coefficient: 11 4.6 ­ Linear Regression and Median Fit Lines Regression Line Median Fit Line Correlation Coefficient 12 4.6 ­ Linear Regression and Median Fit Lines Regression Line Median Fit Line Correlation Coefficient 13.