Maths Made Easy Forums Standard Data & Statistics Least Squares Regression

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• 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,  sx = 7.4443cm,  $$\bar{y}$$  = 6 5.4545cm,  sy = 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

• What is the y-intercept of the least squares regression line given m = 0.9, $$\bar{x}=40.10$$, and $$\bar{y}=60.44$$?
$$y-intercept = \bar{y}-m\bar{x}$$

y-intercept = 60.44 – 0.9 × 40.10

y-intercept = 24.35