15. A study was designed specifically to examine the relationship of human brain size and body size to the intelligence performance. A sample of healthy 38 college students was drawn with age of mean 18.9 years and standard deviation 0.6 years, respectively. In this study, the performance IQ scores (PIQ) based on the revised Wechsler Adult Intelligence Scale is used to measure the individual's intelligence. The brain size is based on the count obtained from magnetic resonance imaging (MRI) scans (in 10,000 counts), meanwhile the height and weight of the students are measured in cm and kg, respectively. The following figure shows the Microsoft Excel Output of multiple regression analysis when all the three predictor variables are used to investigate the PIQ of the students. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.5431 0.2949 0.2327 19.7944 38 ANOVA df MS Significance F Regression Residual Total 3 5572.7444 1857.5815 4.7409 0.0072 34 13321.8082 391.8179 37 18894.5526 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept Brain size Height Weight 111.3536 62.9711 1.7683 0.0860 -16.6191 239.3263 -16.6191 239.3263 2.0604 0.5634 3.6567 0.0009 0.9153 3.2054 0.9153 3.2054 -1.0756 0.4840 -2.2221 0.0330 -2.0592 -0.0919 -2.0592 -0.0919 0.0012 0.4345 0.0028 0.9977 -0.8817 0.8842 -0.8817 0.8842 (i) What can you conclude from the ANOVA table at 5% significance level? Use P-value method. (ii) The following table summarises the multiple regression analysis for the PIQ score to brain size (B), height (H) and weight (W).
15. A study was designed specifically to examine the relationship of human brain size and body size to the intelligence performance. A sample of healthy 38 college students was drawn with age of mean 18.9 years and standard deviation 0.6 years, respectively. In this study, the performance IQ scores (PIQ) based on the revised Wechsler Adult Intelligence Scale is used to measure the individual's intelligence. The brain size is based on the count obtained from magnetic resonance imaging (MRI) scans (in 10,000 counts), meanwhile the height and weight of the students are measured in cm and kg, respectively. The following figure shows the Microsoft Excel Output of multiple regression analysis when all the three predictor variables are used to investigate the PIQ of the students. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.5431 0.2949 0.2327 19.7944 38 ANOVA df MS Significance F Regression Residual Total 3 5572.7444 1857.5815 4.7409 0.0072 34 13321.8082 391.8179 37 18894.5526 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept Brain size Height Weight 111.3536 62.9711 1.7683 0.0860 -16.6191 239.3263 -16.6191 239.3263 2.0604 0.5634 3.6567 0.0009 0.9153 3.2054 0.9153 3.2054 -1.0756 0.4840 -2.2221 0.0330 -2.0592 -0.0919 -2.0592 -0.0919 0.0012 0.4345 0.0028 0.9977 -0.8817 0.8842 -0.8817 0.8842 (i) What can you conclude from the ANOVA table at 5% significance level? Use P-value method. (ii) The following table summarises the multiple regression analysis for the PIQ score to brain size (B), height (H) and weight (W).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
100%
LINEAR
Transcribed Image Text:Variables P-value
Adjusted
Regression equation
B
0.0193
0.1427
0.1189
ŷ = 4.6519+1.1766 B
0.5780
0.0087
-0.0189
ŷ =147.4067– 0.2075 H
W
0.9880
0.0000
-0.0277
ŷ =110.9769 +0.0053 W
|В, Н
0.0022
0.2949
0.2546
ŷ =111.2757 +2.0606 B-1.0747H
В, W
0.0237
0.1925
0.1464
ŷ = 4.7520+1.5925 B-0.5518 W
H, W
0.7322
0.0176
-0.0385
ŷ =164.0402 - 0.4141H+0.2813 W
В, Н, W
ŷ =111.3536+2.0604B–1.0756H+ 0.0012 W
0.0072
0.2949
0.2327
Determine the best regression model for examining the intelligence performance.
Give the appropriate reasons for the chosen model.
Transcribed Image Text:A study was designed specifically to examine the relationship of human brain size and
body size to the intelligence performance. A sample of healthy 38 college students was
drawn with age of mean 18.9 years and standard deviation 0.6 years, respectively. In this
study, the performance IQ scores (PIQ) based on the revised Wechsler Adult Intelligence
Scale is used to measure the individual's intelligence. The brain size is based on the
count obtained from magnetic resonance imaging (MRI) scans (in 10,000 counts),
meanwhile the height and weight of the students are measured in cm and kg, respectively.
The following figure shows the Microsoft Excel Output of multiple regression analysis
when all the three predictor variables are used to investigate the PIQ of the students.
15.
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.5431
0.2949
0.2327
19.7944
38
ANOVA
df
MS
F
Significance F
Regression
3
5572.7444 1857.5815
4.7409
0.0072
Residual
34
13321.8082 391.8179
Total
37
18894.5526
Coefficients Standard Error
t Stat
P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept
111.3536
62.9711
1.7683
0.0860
-16.6191
239.3263
-16.6191
239.3263
Brain size
Height
Weight
2.0604
0.5634
3.6567
0.0009
0.9153
3.2054
0.9153
3.2054
-1.0756
0.4840
-2.2221
0.0330
-2.0592
-0.0919
-2.0592
-0.0919
0.0012
0.4345
0.0028
0.9977
-0.8817
0.8842
-0.8817
0.8842
(i)
What can you conclude from the ANOVA table at 5% significance level? Use
P-value method.
The following table summarises the multiple regression analysis for the PIQ score
to brain size (B), height (H) and weight (W).
(ii)
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