The table below gives the bushels of corn per acre resulting from the use of various amounts of fertilizer in pounds per acre:

Question

n (1st column) BUSHELS OF CORN PRODUCED (Y) (2nd column) AMOUNT FERTILIZER USED (X) (3rd column)

1. 1 (n) 4 (y) 6 (x)
2. 2 44 10
3. 3 46 12
4. 4 48 14
5. 5 52 16
6. 6 58 18
7. 7 60 22
8. 8 68 24
9. 9 74 26
10. 10 80 32

a. Draw a scatter plot for the given data.

b. Economics teaches us that production is a function of inputs. Find linear equation between the two variables using the method of least squares.

c. Compute for the coefficient of correlation r and interpret.

d. What would be the yield if 35 pounds of fertilizer will be used?

Answer 1

a) Draw a y-axis (vertical) for bushels of corn from 0 to 100 with tick marks at 10, 20, 30, ..., 80, and 90.

Draw an x-axis (horizontal) for fertilizer from 0 to 40 with tick marks at 5, 10, 15, ... , 30, and 35.

Mark an X at the intersection of every pair of (x, y), e.g. (x=6, y=4) up to (x=32, y=80).

b) The linear equation is y=10.025 + 2.410*x

c) The correlation coefficient r = 0.9116. This suggests the linear relationship between x and y is very strong.

d) In b) the linear equation was found to be y (yield) = 10.025 + 2.410*x (fertilizer)

If x is given as 35, the y = 10.025 + 2.410*35 = 94.375 bushels.