In their book “Introduction to Linear Regression Analysis” (5th edition, Wiley,
ID: 2929729 • Letter: I
Question
In their book “Introduction to Linear Regression Analysis” (5th edition, Wiley, 2012), Montgomery, Peck, and Vining presented measurements on NbOCl 3 concentration from a tube-flow reactor experiment. The data, in gram-mole per liter × 10 3, are asfollows:
450 450 473 507 457 452 453 1215 1256 1145 1085 1066 1111 1364 1254 1396 1575 1617 1733 2753 3186 3227 3469 1911 2588 2635 2725.
A stem-and-leaf diagram for the data has been given below. Use the diagram to answer questions
The decimal point is 2 digit(s) to the right of the |
4 | 5555671
6 |
8 |
10 | 7915
12 | 2566
14 | 08
16 | 23
18 | 1
20 |
22 |
24 | 9
26 | 435
28 |
30 | 9
32 | 3
34 | 7
(a) What are the readings of the first and last data in the stem-and-leaf diagram?
(b) Comment on the shape of the distribution and outliers.
(c) Which one do you think has a bigger value, the sample mean or the sample median? Explain.
(d) Do you think the sample standard deviation of the data is big or small? Explain.
(e) Use R to draw a stem -and -leaf diagram for the data as the one shown above. Show R codes and outputs. (if you cannot do R part it is OK!)
(f) Where are the observations 1111, 1364 and 2725 located in the stem-and-leaf diagram, respectively? Circle them out in the stem-and
-leaf diagram that you produced in part (e).
(g) In order to construct a frequency and relative frequency distribution table for the NbOCl 3 concentration data, we need to determine K, the number of class intervals and w, the width of each class interval. Use the method discussed in class to determine K and w.
(h) Construct a frequency and relative frequency distribution table for the NbOCl 3 concentration data by hand using the results in part g
(i) Construct a relative frequency histogram for the NbOCl 3 concentration data by hand based on your table in part h.
(j) Comment on the shape of the distribution for the NbOCl 3 concentration data based on your histogram in part i.
(k) Construct a frequency histogram for the NbOCl 3 concentration data using R. Attach the codes and output.
(l)Find the third quartile and the 80th percentile for the NbOCl 3 concentration data by hand
Explanation / Answer
a) First entry: 450
Last Entry: 3470
b) The distribution is skewed to the right because the right tail is longer than left tail. There doesn't seem to be any outlier.
c) Since the distribution is skewed right, the mean will be bigger as compared to median because mean is affected by extreme values and the extreme values on the right will pull the mean value towards right i.e. mean value will be higher.
d) The data spread is high and therefore, the standard deviation will be big.