) From the Excel output, fit a regression model using aptitude test 1 score as X1 and aptitude test 2 score as X2. ii) Interpret the coefficient of X1 and X2. iii) Calculate the adjusted R square for this regression model. iv) Test the overall significance of this regression model at # = 0.05 v) Test the significance of X1 (aptitude test 1 score) and X2 (aptitude test
) From the Excel output, fit a regression model using aptitude test 1 score as X1 and aptitude test 2 score as X2. ii) Interpret the coefficient of X1 and X2. iii) Calculate the adjusted R square for this regression model. iv) Test the overall significance of this regression model at # = 0.05 v) Test the significance of X1 (aptitude test 1 score) and X2 (aptitude test
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Answer these questions from the information from images
i) From the Excel output, fit a regression model using aptitude test 1 score as X1 and aptitude test 2 score as X2.
ii) Interpret the coefficient of X1 and X2.
iii) Calculate the adjusted R square for this regression model.
iv) Test the overall significance of this regression model at # = 0.05
v) Test the significance of X1 (aptitude test 1 score) and X2 (aptitude test 2 score) individually in the regression model at # = 0.05
vi) Estimate the job proficiency score with aptitude test 1 score is 111 marks and aptitude test 2 score is 97 marks.
c) Comparing regression model in (a) and (b), which regression model should be used by the researcher?
Transcribed Image Text:Q6
A personnel officer in a governmental agency administered two newly developed aptitude tests
to a random sample of 13 applicants for entry-level positions in the agency. For the purpose of
the study, all 13 applicants were accepted for positions irrespective of their test scores. After a
probationary period, each applicant was rated for proficiency on the job.
The scores on the two tests (x1, x2) and the job proficiency score (y) for the 13 employees are in
the following:
Job
Aptitude
Aptitude
proficiency test 1
test 2
score (y)
Score (x1)
Score (x2)
88
110
100
80
97
99
96
107
103
76
117
93
80
101
95
73
85
95
58
77
80
116
122
116
104
119
106
99
89
105
64
81
90
126
120
113
94
121
96
Transcribed Image Text:a i) Fit a regression line using job proficiency score as Y and aptitude test 1 score as X. Use
calculator to find the a and b to do so.
ii) Find the coefficient of correlation in this regression model. Interpret its meaning.
iii) Find the coefficient of determination in this regression model. Interpret its meaning.
b) Now the personnel officer wants to include one more variable, aptitude test 2 score, in the
regression model. Thus he obtains the following Excel output using both aptitude test 1 score
and aptitude test 2 score as independent variables:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.95899685
R Square
0.91967496
Adjusted R Square
Standard Error
6.12488914
Observations
13
ANOVA
df
SS
MS
F
Significance F
Regression
2
4295.165022
Residual
10
375.1426698
Total
12
4670.307692
Coefficients Standard Error
t Stat
P-value
Lower 95% Upper 95%
Lower 95.0% Upper 95.0%
Intercept
-102.05967
18.41703463
Aptitude test 1 score (x1) 0.26091492
Aptitude test 2 score (x2) 1.64956174
0.144093118
0.245511906
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