The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), x 5 15 30 40 60 84 105 Well-Being Index Score, y 69.1 68.0 66.8 66.1 64.9 64.1 62.0 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.
Accepted Solution
A:
Answer:[tex]y=-0.065x+69.022[/tex]Step-by-step explanation:The given data table isTime (in minutes) x : 5 15 30 40 60 84 105Well-Being Index Score y : 69.1 68.0 66.8 66.1 64.9 64.1 62.0We need to find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.The general form of least-squares regression line[tex]y=bx+a[/tex] .... (1)where, a is y-intercept and b is slope.[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex][tex]a=\overline{y}-b\overline{x}[/tex]Using graphing calculator we get[tex]b=0.0653469053052\approx 0.065[/tex][tex]a=69.0218001284\approx 69.022[/tex]Substitute the values of a and b in equation (1).[tex]y=-0.065x+69.022[/tex]Therefore, the least-squares regression line is y=-0.065x+69.022.