For the plant emission data below for 11 potato plants deter

For the plant emission data below for 11 potato plants, determine the following (write answers in provided sections): PLANT WEIGHT (X) In grams, QUANTITY OF VOLATILE COMPOUNDS (Y)In hundreds of nanograms

x ------y

57---- 8.0

85----22.0

57----10.5

65---- 22.5

52-----12.0

67-----11.5

62-----7.5

80-----13.0

77----16.5

53-----21.0

68-----12.0

a) Write the regression equation __

b) Write the values of the constant b0 and slope b1 __

c) Predict the quantity of volatile compounds emitted by a potato plant that weights 75 grams

Correlation Analysis (Using the Same Data as Above). Instructions: • Store the data in two variables. • Choose Stat -> Basic Statistics… -> Correlation. • Specify the variable names in the Variables textbox. • Clock OK. For the plant emission data above, determine the following (write answers in provided sections):

a) Find the Pearson correlation of PLANT WEIGHT __ and QUANTITY OF VOLATILE COMPOUNDS

b) Interpret r __

c) Find the coefficient of determination r2 __

d) Interpret r2 __

Solution

X

57

85

57

65

52

67

62

80

77

53

68

Y

8.0

22.0

10.5

22.5

12.0

11.5

7.5

13.0

16.5

21.0

12.0

X² = 48747        X = 723               Y² =2523.25      Y = 156.5            XY = 10486

X = 65.7273         Y = 14.2273          r_xy = 0.3311          _x = 10.5578        _y = 5.1933

Y = b₀ + b₁(x)

The normal equations are

   Y = n b₀ + b₁ x   

11(b0) + b1(723) = 156.5-----------1 equation

   XY = x b₀ + X² b₁

(723)b0 + 48747 (b1) = 10486-----------2 equation

Solve the above two normal equations we get the values of b0 and b1

b0 = 3.5237    b1 = 0.1628

the regression line equations are

X on Y ------   (X - X) = r_xy (_x / _y) (Y - Y)

                  (X - 65.7273) = 0.3311 (10.5578 / 5.1934) (Y – 14.2273)                                

    (X – 65.7273 ) = (0.6731)(Y – 14.2273)

                   X = (0.6731) Y + 56.1509

Y on X ------   (Y - Y) = r_xy ( _y / _x ) (X - X)

             (Y – 14.2273 ) = 0.3311 ( 5.1934 / 10.5578) (X – 65.7273)

              (Y – 14.2273 ) = (0.1629) (X – 65.7273)

                Y =(0.1629) X + 3.5224

When X = 75

Y =(0.1629) (75) + 3.5224

Y = 15.7399

Coefficient of determination r² = b_xy    *     b_yx

                                                                = (0.1629) (0.6731)

                                                               = 0.1096

X	57	85	57	65	52	67	62	80	77	53	68
Y	8.0	22.0	10.5	22.5	12.0	11.5	7.5	13.0	16.5	21.0	12.0