Answered: uccess in obtaining grant support (X3).…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A researcher in a scientific foundation wished to evaluate the relation between intermediate and senior level annual salaries of research mathematician (Y, in thousand dollars) and an index of publication quality (X1), the number of years experience (X2), and an index of success in obtaining grant support (X3). A. Determine the R2 and adjusted R2. B. Determine the significant factors. C. Determine if the residual follows a normal distribution . Determine if the variance is constant over time. Find the leasts-squares regression equation. The data for a sample of 24 intermediate and senior level research mathematicians follow.

Salary (in thousand 8)
33.2
40.3
38.7
46.8
41.4
37.5
39.0
40.7
30.1
52.9
38.2
31.8
43.3
44.1
42.8
33.6
34.2
48.0
38.0
35.9
40.4
36.8
45.2
35.1
Publication Quality
3.5
5.3
5.1
5.8
4.2
6.0
6.8
5.5
3.1
7.2
4.5
4.9
8.0
6.5
6.6
3.7
6.2
7.0
4.0
4.5
5.9
5.6
4.8
3.9
No. of Years Experience
9
20
18
33
31
13
25
30
5
47
25
11
23
35
39
21
7
40
35
23
33
27
34
15
Grant Support
6.1
6.4
7.4
6.7
7.5
5.9
6.0
4.0
5.8
8.3
5.0
6.4
7.6
7.0
5.0
5.5
7.0
6.0
3.5
4.9
4.3
8.0
5.0

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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