Question

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

Answer 1

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

> mean (tea) [1] 70.68087 median (tea) 1] 68. 31 mfv1 (tea) [1] 42.12 range (tea) [1] 42.12 111.32 mean (coffee) [1] 100.1296 median (coffee) [1] 101.31 mfv1 (coffee) [1] 87.62 range (coffee) [1] 87.62 106.30

> summary (tea) Min. 1st Qu. Median Mean 3rd Qu 83. 36 111.30 мах. 42. 12 56. 18 68. 31 70. 68 > summary (coffee) Min. 1st Qu. Median Mean 3rd Qu. Мах. 87.62 96. 56 101. 30 100.10 104.00 106. 30 > 83. 36-56.18 [1] 27.18 > 104.00-96. 56 [1] 7.44 sd(tea) [1] 19. 67633 sd(coffee) [1] 4.997177

range(tea)=111.32-42.12=69.2

range(coffee)=106.30-87.62=18.68

Histogram of coffee 85 90 95 100 105 110 coffee Frequency 9

Here the model interval length is 5 units.

Histogram of tea LO 80 40 60 100 120 tea Frequency 9

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.

95 000 06

Boxplot of tea

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

00 08 09 O40

90 95 100 105 coffee C 08 09 O40 00 tea

1995 2000 2005 2010 2015 year coffee 06 105 000


1995 2000 2005 2010 2015 year 00 08 09 40 tea

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

Call 1m (formula coffee tea) Residuals: Min 1Q Median 3Q Маx -8.002 -1.819 1.099 2.032 4.885 Coefficients: Estimate Std. Error t value Pr>t). (Intercept) 86.3200 2. 5935 33.283 2e-16 tea 0.1954 0.0354 5.518 1.78e-05 Signif. codes: 0 0.01 0.05 .0.1 0.001 1 Residual standard error: 3.267 on 21 degrees of freedom 0.5919, Multiple R-squared: F-statistic: 30.45 on 1 and 21 DF, Adjusted R-squared: 0.5724 p-value 1.781e-05

The obtained model is:

coffee=86.3200+0.1954*tea