Answer:
[tex]y=-0.065x+69.022[/tex]
Step-by-step explanation:
The given data table is
Time (in 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
We 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.
