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Tagged: least squares, regression, y-intercept
Researchers have found a correlation between obesity and the number of hours per day children spend in front of a video screen.
Hours : $$\bar{H}=2.5,s_H=1.29$$ Kg over average weight: $$\bar{W}=2.17,s_W=1.05$$
Find the equation of the least-squares line of best fit given the value of r = 0.955.
y = mx + b ⇔ W = mH + b
Find m using the formula: $$m=r\times\frac{s_y}{s_x}$$
$$m=0.995\times\frac{1.05}{1.29}$$
m = 0.81
Find b using the formula: $$\overline{y} -m\overline{x}$$
$$b=2.17-0.81\times 2.5$$
b = 0.145
W = 0.81H + 0.145
The heights (x) and weights (y) of 11 people have been recorded, and the values of the following statistics determined:
$$\bar{x}$$ = 173.2727cm, s_{x} = 7.4443cm, $$\bar{y}$$ = 6 5.4545cm, s_{y} = 7.5943cm r = 0.8502.
Find the equation of the least squares regression line that will enable weight to be predicted from height.
y = mx + b
Find m using the formula: $$m=r\times\frac{s_y}{s_x}$$
$$m=0.8502\times\frac{7.5943}{7.443}$$
m = 0.867
Find b using the formula: $$\overline{y} -m\overline{x}$$
$$b=65.4545-0.867\times 173.2727$$
b = -84.773
y = 0.8671x – 84.773