Question

In: Statistics and Probability

Consider the following Data: Year Tea (L per person) Coffee (L per person) 1994 42.4 95.85...

Consider the following Data:

Year

Tea
(L per person)

Coffee
(L per person)

1994

42.4

95.85

1995

42.12

97.28

1996

47.61

87.62

1997

60.86

92.04

1998

55.58

99.21

1999

50.61

95.63

2000

49.89

97.42

2001

56.77

93.93

2002

62.53

95.67

2003

68.31

99.25

2004

69.88

101.31

2005

72.99

101.68

2006

71.36

104.02

2007

90.78

106.09

2008

74.7

105.8

2009

67.15

102.15

2010

67.03

101.15

2011

87.83

104.05

2012

93.4

102.7

2013

78.9

105.28

2014

111.32

106.3

2015

98.39

104.96

2016

105.25

103.57

By using the definition and discussing what is relevant to the situation, interpret each of the following for both the coffee and tea data. Also, compare each for coffee and tea. Be sure to include the relevant information (state the value of or, in the case of the distribution, include the graphs) with each component.

  1. Mean
  2. Median
  3. Modal Interval
  4. Range
  5. IQR
  6. Standard Deviation
  7. Distribution of histogram and box plot
  8. Slope of each linear model
  9. Y-intercept of Coffee vs. Tea
  10. Correlation coefficient for each linear model
  11. Relevant interpolations or extrapolations
  12. Correlation type for coffee and tea

Solutions

Expert Solution

Here I attach the R code with output

tea=c(42.4,42.12,47.61,60.86,55.58,50.61,49.89,56.77,62.53,68.31,69.88,72.99,71.36,90.78,74.7,67.15,67.03,87.83,93.4,78.9,111.32,98.39,105.25)
coffee=c(95.85,97.28,87.62,92.04,99.21,95.63,97.42,93.93,95.67,99.27,101.31,101.68,104.02,106.09,105.8,102.15,101.15,104.05,102.7,105.28,106.3,104.96,103.57)

year=c(1994:2016)  
mean(tea)
median(tea)
mfv1(tea)
range(tea)
mean(coffee)
median(coffee)
mfv1(coffee)

summary(tea)
summary(coffee)
IQRtea=83.36-56.18=27.18
IQRcoffee=104.00-96.56=7.44
sd(tea)
sd(coffee)

range(coffee)
hist(coffee)
hist(tea)
boxplot(coffee)
boxplot(tea)
plot(coffee,tea)

plot(year,coffee)
plot(year,tea)

m=lm(coffee~tea)
summary(m)
cor(coffee,tea)

The measure of central tendency are mean, median , mode(mfv-most frequent observation) etc..

Measure of spread is range

range(tea)=111.32-42.12=69.2

range(coffee)=106.30-87.62=18.68

Here the model interval length is 5 units.

Here the model interval length is taken as 10 units.

Boxplot of coffee

From the plot it is clear that the distribution is negatively skewed and there is no outliers in the data.

Boxplot of tea

From the plot we can infer that the distribution is positively skewed and there is no outliers in the model.


The correlation between Coffee and tea is 0.769, which implies there is positive linear relatioship exist between the variable tea and coffee.

The obtained model is:

coffee=86.3200+0.1954*tea


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