Question

Complete parts​ (a) through​ (c) using the following data.

Row 1 2 2 2 5 5 5 5 6 7 7
Row 2 92 82 83 79 90 73 79 82 59 70 ​

Construct a scatter plot of the data and draw the regression line. Plot Row 1 on the horizontal axis and Row 2 on the vertical axis.

(a) Find the equation of the regression line for the given​ data, letting Row 1 represent the​ x-values and Row 2 the​ y-values. Sketch a scatter plot of the data and draw the regression line. Input the values of the slope and intercept for the regression line when Row 1 represents the​ x-values.

​(Round to three decimal places as​ needed.)

​(b) Find the equation of the regression line for the given​ data, letting Row 2 represent the​ x-values and Row 1 the​ y-values.

Sketch a scatter plot of the data and draw the regression line. Input the values of the slope and intercept for the regression line when Row 2 represents the​ x-values.

y = x( ) +( )

​(Round to three decimal places as​ needed.)

Answer 1

X	y	(x-xbar)^2	(x-xbar)(y-ybar)
2 2 2 5 5 5 5 6 7 7 M: 4.6	92 82 83 79 90 73 79 82 59 70 M: 78.9	6.76 6.76 6.76 0.16 0.16 0.16 0.16 1.96 5.76 5.76 SS: 34.4	-34.06 -8.06 -10.66 0.04 4.44 -2.36 0.04 4.34 -47.76 -21.36 SP: -115.4

a) regression equation

  Sum of X = 46
Sum of Y = 789
Mean X = 4.6
Mean Y = 78.9
Sum of squares (SS_X) = 34.4
Sum of products (SP) = -115.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = -115.4/34.4 = -3.355

a = M_Y - bM_X = 78.9 - (-3.35*4.6) = 94.331

ŷ = -3.355X + 94.331

Scatter plot

B) Sum of X = 789
Sum of Y = 46
Mean X = 78.9
Mean Y = 4.6
Sum of squares (SS_X) = 840.9
Sum of products (SP) = -115.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = -115.4/840.9 = -0.137

a = M_Y - bM_X = 4.6 - (-0.14*78.9) = 15.428

ŷ = -0.137X + 15.428

Scatter diagram