Frequency Distribution, Regression Analysis, ANOVA and Interpretation of Results

Question 1 Solution:
(a)
Here our variable under study is furniture order (in $)
For constructing frequency distribution, we need to find minimum and maximum observation
from the data. As the class with is given as 50.
Minimum = 123
Maximum = 490
So, Range of the data = Maximum – Minimum = 490 -123 = 367
Number of classes = (Range of the data) / (class width) = 367 / 50 = 7.340
So we make 7.37 ≈ 8 classes so that minimum of the data included in the first class and
maximum will be in the last class
So the 8 classes are as follows:
120 – 170 170 - 220 220 – 270 270 - 320 320 - 370 370 - 420 420 - 470 470 - 520
Frequency distribution:
Frequency of any particular class is the count of observation in that class i.e. number of data
points which greater than or equal to lower boundary of class and less that upper boundary of
class.
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Class-
Interval Frequency
120 - 170 8
170 - 220 15
220 - 270 12
270 - 320 4
320 - 370 5
370 - 420 2
420 - 470 2
470 - 520 2
Total 50
Relative Frequency distribution:
Relative frequency of any class is portion of frequency of that class with total frequency. Here
the total frequency i.e. Total number of observation is 50.
Class-Interval Relative Frequency
120 - 170 0.16
170 - 220 0.30
220 - 270 0.24
270 - 320 0.08
320 - 370 0.10
370 - 420 0.04
420 - 470 0.04
470 - 520 0.04
Total 1.00
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Percent Frequency distribution:
Percent frequency of any particular class = Relative frequency of that class × 100
Class
Interval Percent Frequency
120 - 170 16
170 - 220 30
220 - 270 24
270 - 320 8
320 - 370 10
370 - 420 4
420 - 470 4
470 - 520 4
Total 100
(b)
Figure: Percent Frequency Histogram
One can see there is positive skewness in the data.
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(c)
Apart from the shape of the distribution, mean is always good measure for all shaped
distribution where it is exist.
For given observations,
Mean=251.46, Median = 228.5 and Mode = 231
Question 2 Solution :
It is the problem of simple linear regression.
Response variable is Demand and Predictor (independent) variable is unit price.
Y: Demand and X: Unit Price
(a)
Here we test the null hypothesis that Y and X are not related against the alternative hypothesis
that Y and X are related.
To test this hypothesis, we need to complete the given incomplete ANOVA
SS = sum of square and
df = degrees of freedom.
Given values in ANOVA:
sum of square of regression = SSReg = 5048.818
sum of square of error = SSError = 3132.661
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