Assignment 6
Due date: 7 December 2009
Total number of points: 22
Q
1.
(12.5, 12.14, 12.21, 12.28) Twenty plots were randomly chosen in a large field of corn. For each plot, the plant
density (number of plants in the plot) and the mean cob weight (g of grain per cob) were observed. The following
quantities were computed:
¯
x
= 128
.
95
,
¯
y
= 224
.
1
(
x
i

¯
x
)
2
= 20
,
209
.
0
,
(
y
i

¯
y
)
2
= 11
,
831
.
8
(
x
i

¯
x
)(
y
i

¯
y
) =

14
,
563
.
1
,
SS(resid) = 1
,
337
.
3
(a)
Find the regression line. Take cob weight as
Y
.
(b)
Interpret the value of the slope.
(c)
Estimate
σ
, standard deviation of the errors.
(d)
Estimate the mean cob weight to be expected in a plot containing 100 plants.
(e)
Calculate the standard error of the slope.
(f)
Construct 95% confidence interval for the slope.
(g)
Calculate correlation coefficient.
(h)
Calculate coefficient of determination. Interpret.
Solution to Q1:
(a)
ˆ
Y
= 316
.
4

0
.
7206
X
(b)
If plant density increases by 1 plant per plot, cob weight decreases by 0.72 gm of grain per cob, on
average.
(c)
s
Y

X
=
1337
.
3
/
18 = 8
.
6 gm
(d)
316
.
4

0
.
7206
*
100 = 244
.
34 gm
(e)
8
.
6
/
√
20209 = 0
.
0605
(f)

0
.
7206
±
2
.
101
×
0
.
0605
(g)
0.942
(h)
R
2
= 0
.
942
2
= 0
.
89. 89% of variability in cob weight can be explained by the linear relationship with
number of plants.
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 Spring '08
 Statistics, Regression Analysis, Standard Deviation, Phenytoin, cob weight

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