Question

Laetisaric acid is a compound that holds promise for control of fungus disease in crop plants. The accompanying data show the results of growing the fungus Pythium ultimum in various concentrations of laetisaric acid. Each growth value is the average of four radial measurements of P. ultimum colony grown in a petri dish for 24 hours; there were two petri dishes at each concentration.

Laetisaric acid X | Fungus Growth Y
0 | 33.3
0 | 31.0
3 | 29.8
3 | 27.8
6 | 28.0
6 | 29.0
10 | 25.5
10 | 23.8
20 | 18.3
20 | 15.5
30 | 11.7
30 | 10.0
Mean
11.500 | 23.642
sd
10.884 | 7.8471
v. State the slope and interpret its meaning in context.
vi. SS(resid)=16.7812. Use this to compute se.
vii. Show what needs to be calculated for a 95% prediction interval for x = 20. (fill in all the values in the equation but do not evaluate.)

Answer 1

r = - 0.98754

Answer:

Slope = - 0.7120

SE = 1.295

Explanation:

Given the data:

0 | 33.3

0 | 31.0

3 | 29.8

3 | 27.8

6 | 28.0

6 | 29.0

10 | 25.5

10 | 23.8

20 | 18.3

20 | 15.5

30 | 11.7

Using the relation to Obtian the slope :

Slope, b = r(Sy/Sx)

r = correlation Coefficient ; Sy = standard deviation of Y - values ; Sx = standard deviation of X-values

r = - 0.98754

Slope, b = - 0.98754(7.8471 / 10.884) = - 0.7120

SE = √SSresidual / df

df = n - 2 = 12 - 2 = 10

SSresidual = 16.7812

SE = √(16.7812/ 10)

SE = 1.295