Answered: A business statistics professor would…

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 business statistics professor would like to develop a regression model to predict the exam scores for students based on their current GPAs, the number of hours they studied for the exam, and the number of times they were absent during the semester. The data for these variables is attached.

a) Run the multiple regression in Excel. Hint: set x₁ = GPA, x₂ = Hours, X₃ = Absences.

b) Find the R² and explain its meaning.

c) Explain the outcome of the F test. What does it mean?

d) Explain the outcomes of the t tests for the slope coefficients.

e) Write out the regression equation.

f) Explain the meanings of the slope coefficients.

Score
GPA
Hours
Absences
68
2.53
3.00
69
2.25
4.00
3
70
2.60
2.50
1
71
3.10
0.50
74
3.08
6.00
4
77
2.75
3.50
6
77
3.35
1.50
78
2.98
3.00
3
78
2.99
2.00
3
79
2.84
2.50
2
79
2.80
4.50
82
3.44
7.00
1
83
3.25
3.00
1
84
3.15
3.00
4
84
3.18
5.50
84
2.95
2.00
84
2.71
4.00
1
85
3.20
4.50
85
3.75
2.00
85
3.57
3.50
2
86
2.92
6.00
1
86
3.04
6.50
1
86
3.16
5.00
87
3.89
7.50
4
87
3.54
4.00
89
3.33
6.50
1
89
3.66
5.00
90
2.87
3.50
90
3.40
6.00
1
91
3.22
4.50
91
3.79
7.00
92
3.93
6.00
2
92
4.00
5.00
92
3.60
6.50
1
93
2.98
4.00
2
94
3.26
6.50
98
2.88
3.50
99
3.73
5.00
1
100
3.48
6.50
1
100
3.00
7.00

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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