Question

A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y (b) Given that x = 3.5000, 5x = 2.2583, y = 3.8667, 5y = 1.8822, and r= -0.9552, determine the least-squares regression line (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 1 1 3 4 6 6 5.0 6.4 4.9 3.3 1.6 2.0 у (a) Choose the correct graph below. B ОА. AY Oc. Q AY .. a Q 3 Q Q There appears to be relationship Click to select your answer(s).

Answer 1

a) Scatter plot of X and Y

Scatter plot X vs Y 7 6 5 4 3 2 1 0 0 1 2 3 4 6 7 U

That appears to be negative relationship.

b) given,

$\small \bar{y}$ = 3.8667, $\small \bar{x}$ = 3.5000, Sx = 2.2583, Sy = 1.8822, r = - 0.9552

Slope of the equation,

$\small b = r\frac{ s_{y}}{s_{x}}$

$\small b = -0.9552\frac{ 1.8822}{2.2583}=-0.796$

$\small a = \bar{y}-b \bar{x}$

$\small a = 3.8667-(-0.796)* 3.5000 = 6.653$

Regression equation is given by,

$\small \hat{y} = 6.653 - 0.796 x$

c) least square regression line,

Linear plot 7 6 5 4 3 2 1 0 0 1 2 3 4 6 7 U

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