Question

Tmt	Price ($)	Height (in)	Treatment	Total Stem Caliper (in)	Field	KFC	PiP
Field	106	104	1	6.3	1	0	0
Field	106	100	1	6.7	1	0	0
Field	106	113	1	4.95	1	0	0
Field	106	104	1	4.6	1	0	0
Field	132	129	1	8.4	1	0	0
Field	132	136	1	9	1	0	0
Field	170	154	1	6.6	1	0	0
Field	132	124	1	7.8	1	0	0
Field	106	115	1	6.5	1	0	0
Field	132	130	1	7.8	1	0	0
Field	132	140	1	8.85	1	0	0
Field	132	133	1	5.95	1	0	0
Field	106	109	1	3	1	0	0
Field	106	109	1	7.55	1	0	0
Field	89	101	1	5.35	1	0	0
Field	132	128	1	7.05	1	0	0
Field	106	115	1	5.55	1	0	0
Field	106	116	1	6.9	1	0	0
Field	132	128	1	8.35	1	0	0
Field	132	123	1	9.05	1	0	0
Field	106	116	1	6.3	1	0	0
Field	132	130	1	6.75	1	0	0
Field	132	130	1	5.4	1	0	0
Field	132	132	1	4.8	1	0	0
Field	106	101	1	6.45	1	0	0
KFC	96	116	2	7.3	0	1	0
KFC	119	129	2	4.15	0	1	0
KFC	119	131	2	5.95	0	1	0
KFC	96	100	2	4.7	0	1	0
KFC	96	105	2	5.3	0	1	0
KFC	76	80	2	4.4	0	1	0
KFC	96	108	2	7.25	0	1	0
KFC	76	92	2	6.7	0	1	0
KFC	96	113	2	6.9	0	1	0
KFC	96	101	2	5.15	0	1	0
KFC	96	105	2	4.75	0	1	0
KFC	96	108	2	4.6	0	1	0
KFC	96	101	2	3.3	0	1	0
KFC	76	91	2	5.2	0	1	0
KFC	96	99	2	6.55	0	1	0
KFC	96	110	2	5.65	0	1	0
KFC	119	132	2	8.45	0	1	0
KFC	96	102	2	6.7	0	1	0
KFC	119	129	2	8.75	0	1	0
KFC	119	135	2	8.15	0	1	0
KFC	119	134	2	7.15	0	1	0
KFC	119	131	2	9.35	0	1	0
KFC	119	124	2	7.7	0	1	0
KFC	119	126	2	6.8	0	1	0
KFC	119	131	2	7.35	0	1	0
Pip	69	95	3	5.35	0	0	1
Pip	69	107	3	6.55	0	0	1
Pip	69	97	3	5.55	0	0	1
Pip	69	112	3	7.25	0	0	1
Pip	69	104	3	5.5	0	0	1
Pip	79	114	3	6.45	0	0	1
Pip	69	88	3	3.85	0	0	1
Pip	69	97	3	6.95	0	0	1
Pip	79	115	3	6.6	0	0	1
Pip	99	133	3	5.6	0	0	1
Pip	79	112	3	4.8	0	0	1
Pip	69	87	3	5.65	0	0	1
Pip	79	102	3	6.05	0	0	1
Pip	69	91	3	5.65	0	0	1
Pip	69	90	3	6.25	0	0	1
Pip	69	94	3	5.35	0	0	1
Pip	79	98	3	6.45	0	0	1
Pip	79	100	3	6.2	0	0	1
Pip	69	88	3	5	0	0	1
Pip	79	112	3	5.95	0	0	1
Pip	99	121	3	5.2	0	0	1
Pip	69	92	3	4.8	0	0	1
Pip	69	95	3	6.5	0	0	1
Pip	69	93	3	5.85	0	0	1
Pip	79	118	3	4.7	0	0	1

Research was conducted on different production methods for landscape trees.

Traditionally, trees were planted in the field and then harvested with a large root ball wrapped in

burlap (the Field treatment). This method can remove more than 200 pounds of top soil per tree

from the field. Soil saving methods of production include knit fabric containers (KFC) and pot-inpot

(PiP) treatments. Use the Excel data set, “Tree data.xlsx” to complete the following analyses.

1. Assume that tree price depends on the height. If this is true, then a comparison of means could

be affected by the different tree heights – the results could be biased. Estimate the following

simple regression model (use the third worksheet, Q3 & Q4 – Prices for Regression):

i 0 1 i i Price     Height  

(6) a. Use Excel’s Data Analysis to estimate the model (or Minitab if you have it). Provide a copy

of the regression results.

(4) b. How well does the model explain tree prices? Write a sentence explaining the appropriate

interpretation of the statistic that indicates how well the regression model fits the data.

(4) c. Interpret of the estimate of the population parameter 1  . (What does your estimate tell you

about the relationship between tree height and price?)

9

d. Is the estimated effect of tree height on price statistically significant at the 5% level of

significance? Complete the test, specifically:

(4) i. What is the hypothesis you will test?

(4) ii. What is the critical value for this test?

(4) iii. What is the calculated test statistic?

(4) iv. What is your conclusion? Explain what the test tells you.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.855458
R Square	0.731808
Adjusted R Square	0.728134
Standard Error	12.29374
Observations	75
ANOVA
	df	SS	MS	F	Significance F
Regression	1	30105.25	30105.25	199.1929	1.49E-22
Residual	73	11032.94	151.1361
Total	74	41138.19
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-43.4288	10.20875	-4.25408	6.14E-05	-63.7748	-23.0828
Height (in)	1.272735	0.090178	14.11357	1.49E-22	1.093011	1.45246

From regression output:

price=-43.429+1.273*Height

(4) b. How well does the model explain tree prices? Write a sentence explaining the appropriate

interpretation of the statistic that indicates how well the regression model fits the data.

H0:modei is significant,model fits the data

H1:model is not signifcant

From Anova table

F(1,73)=199.1929

p=0.000

p<0.05

Model is significant.Model fits the data.

(4) c. Interpret of the estimate of the population parameter 1

standard error of estimate =12.29374

(What does your estimate tell you

about the relationship between tree height and price?)

R sq=0.731808

=0.731808*100

=73.18% variation in price is epxlained by height

explained variance by model=73.18%

unexplained variance=100-73.18=26.82%

Is the estimated effect of tree height on price statistically significant at the 5% level of

significance? Complete the test, specifically:

(4) i. What is the hypothesis you will test?

Hypothesis test on slope of regression line

If there is a significant linear relationship between the independent variable ,height and the dependent variable price, the slope will not equal zero.

Ho: = 0

Ha: ≠ 0

The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

(4) iii. What is the calculated test statistic?

t=coefficient/std error=1.272735/0.090178=14.1157

(4) iv. What is your conclusion? Explain what the test tells you.

p=0.0000

p<0.05

Reject null hypothesis.
Accept alternative Hypothesis.

At 5% level of significance ,there is a significant linear relationship between the independent variable ,height and the dependent variable price