Given:
The speed, s, is measured in miles per hour, and distance, y, is measured in yards.
The regression line is given by
[tex]\hat{Y}=4.17+52.45s[/tex] Â Â Â Â ...(i)
To find:
The slope and y-intercept of the regression line.
Solution:
The general form of linear regression line is
[tex]y=a+bx[/tex] Â Â ...(ii)
where x is variable. In the given equation the variable is denoted by s.
On comparing (i) and (ii), we get
[tex]a=4.17, b=52.45[/tex]
It means slope is 52.45 and y-intercept is 4.17.
The slope, b = 52.45, indicates that the distance increases by 52.45 yards for every one mile per hour of speed.
The y-intercept, a = 4.17, is the distance estimated by this model if the speed is zero miles per hour.
Therefore, the correct option is A.