Chapter 8, Problem 8.9CRE

a.

To determine

To construct: A plot using the distribution of neuronal response to a pure tone and find the numerical summary. Also check whether there outliers exist or not, if yes then again find the numerical summary by omitting it and explain their influence.

Explanation of Solution

Given:

The dataset:

Neuron	Tone	Call	Neuron	Tone	Call
1	474	500	20	100	118
2	256	138	21	74	62
3	241	485	22	72	112
4	226	338	23	20	193
5	185	194	24	21	129
6	174	159	25	26	135
7	176	341	26	71	134
8	168	85	27	68	65
9	161	303	28	59	182
10	150	208	29	59	97
11	19	66	30	57	318
12	20	54	31	56	201
13	35	103	32	47	279
14	145	42	33	46	62
15	141	241	34	41	84
16	129	194	35	26	203
17	113	123	36	28	192
18	112	182	37	31	70
19	102	141

Formula used:

The formula to compute the correlation is:

  $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{n(\sum x^2)-{(\sum x)}^2}\sqrt{n(\sum y^2)-{(\sum y)}^2}}$

Graph:

The scatter plot could be constructed as:

  

Interpretation:

From the above scatter plot, it is clear that the value 474 is an outlier because it is far distant from the other values.

Calculation:

The numerical summary is:

  

After removal of outlier, the value of the correlation is:

  

From above output, it is clear that omission of outlier has led the reduction in the value of correlation between the two variables

b.

To determine

To construct: A plot using the distribution of neuronal response to a monkey call and find the numerical summary. Also check whether there outliers exist or not, if yes then again find the numerical summary by omitting it and explain their influence.

Explanation of Solution

Graph:

The scatter plot could be constructed as:

  

Interpretation:

From the above scatter plot, it is clear that the values 484 and 500 are outlier because they are far distant from the other values.

Calculation:

The numerical summary is:

  

After removal of outlier, the value of the correlation is:

  

From above output, it is clear that omission of outlier has led increase in the value of correlation between the two variables

c.

To determine

To construct the pie chart or bar chart to show the proportion of given categories.

Explanation of Solution

Given:

The categories:

Very low birth weight: Less than 1500 grams

Low birth weight: Less than 2500 grams

Normal birth weight: More than 2500 grams

Calculation:

Count of each category:

Category	Frequency	Proportion
Very low birth Weight	57841	0.0144768
Low birth weight	267722	0.0670072
Normal birth weight	3669859	0.918516

Graph:

  

d.

To determine

To check: whether there any relationship exists between the variables call and tone response by constructing scatter plot and explain it. Also, compute the numerical summary, if possible.

Explanation of Solution

Graph:

The scatter plot could be constructed as:

  

Interpretation:

The above scatter plot shows that there is a positive correlation between the two variables despite the presence of outlier in the data set.

Calculation:

The correlation between the two variables can be calculated as: