Question

Height	Fertilizer
20.4	1.9
29.1	5.0
28.2	4.2
24.3	1.3
29.2	4.9
29.8	5.4
34.6	3.1
25.3	0.0
26.2	2.3
25.7	2.5
26.5	0.9
28.6	1.0
25.7	4.5
36.8	3.8
27.2	5.3
33.4	2.3
25.1	4.0
22.1	1.4
40.6	3.9
24.5	4.0
39.7	3.6
21.1	0.6
25.4	1.6
29.6	2.5
27.6	4.5
32.6	3.6
33.5	2.0
22.5	0.0
27.6	2.5
36.4	3.1

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured. A portion of the results is shown in the accompanying table. Height 20.4 29.1 Fertilizer 1.9 5.0 36.4 3.1 Click here for the Excel Data File a. Estimate the linear regression model: Height = B@ + B1Fertilizer + ε. (Round your answers to 2 decimal places.) Height= Fertilizer b-1. Estimate the quadratic regression model: Height = Be + B1Fertilizer + B2Fertilizer2 + ε. (Negative values should be indicated by a minus sign. Round answers to 2 decimal places.) Height Fertilizer + Fertilizer2 а or maximum. (Round b-2. Using the quadratic results, find the fertilizer amount at which the height re coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Fertilizer amount = ounces c. Use the best-fitting model to predict, after a four-month period, the height of a tomato plant that received 3.0 ounces of fertilizer. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Height= inches

Answer 1

from excel: regression: data-data analysis:

a)

Height =24.96+1.29*Fertilizer

b-1)

Height =21.07+5.46*Fertilizer+(-0.76)*Fertilizer²

b-2)

predicted value =-b1/2b2 =-5.456/(2*-0.759) = 3.59 ounces

c)

from quadratic model: height =30.60 inches

(please try 28.83 if this comes wrong )