Mental development in humans is related to the volume of the part of the brain known as the hippocampus. The given regression output shows the mental development index at age 24 months vs. the hippocampus volume in ml at birth for a representative sample of 17 premature infants. MDI_24 By Vol(ml) 2.5- 2.4- 2.3- 2.2- 2.1- 2- 1.9- 1.8- 1.7- 1.6- 1.5+ 50 60 70 80 90 100 110 12 Vol(ml) Regression Analysis MDI_24M0 = 1.1359094 + 0.0093475*HippoVol Summary of Fit RSquare RSquare Adj S 0.265 0.216 0.223 1.97758 Mean of Response NObservations 17 MDI 24MO

Mental development in humans is related to the volume of the part of the brain known as the hippocampus. The given regression output shows the mental development index at age 24 months vs. the hippocampus volume in ml at birth for a representative sample of 17 premature infants. MDI_24 By Vol(ml) 2.5- 2.4- 2.3- 2.2- 2.1- 2- 1.9- 1.8- 1.7- 1.6- 1.5+ 50 60 70 80 90 100 110 12 Vol(ml) Regression Analysis MDI_24M0 = 1.1359094 + 0.0093475*HippoVol Summary of Fit RSquare RSquare Adj S 0.265 0.216 0.223 1.97758 Mean of Response NObservations 17 MDI 24MO

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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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

Mental development in humans is related to the
volume of the part of the brain known as the
hippocampus. The given regression output shows the
mental development index at age 24 months vs. the
hippocampus volume in ml at birth for a
representative sample of 17 premature infants.
MDI_24 By Vol(ml)
2.5
2.4-
2.3-
2.2-
2.1-
2-
1.9-
1.8-
1.7-
1.6-
1.5-
50
60
70
80
90
100
110
12
Vol(ml)
Regression Analysis
MDI_24MO = 1.1359094 + 0.0093475*HippoVol
Summary of Fit
RSquare
RSquare Adj
S
Mean of Response
0.265
0.216
0.223
1.97758
NObservations
17
Analysis of Variance
Source
Model
DF Sum of Squares
1 0.268
Mean Square F Ratio
0.268
5.4023
MDI_24M0

Regression Analysis
MDI_24M0 = 1.1359094 + 0.0093475*HippoVol
Summary of Fit
RSquare
RSquare Adj
S
0.265
0.216
0.223
Mean of Response
NObservations
1.97758
17
Analysis of Variance
Source
DF Sum of Squares
Mean Square F Ratio
0.268
Model
1
0.268
5.4023
Error
15 0.744
0.050
Prob >F
C. Total
16 1.013
0.0346*
Parameter Estimates
Term
Estimate
Std Error tRatio
Prob>|t|
0.0073*
Intercept
HippoVol
1.1359
0.366
3.10
0.0093
0.004
2.32
0.0346*
a) What is the equation of the estimated regression
line?
b) What is the calculated value of sb?
c) What is the calculated value of se?
d) In a few sentences, interpret se in the context of
this problem.
e) Using the computer output above, perform the
Model Utility Test at the .05 level of significance.
f) Construct a 95% confidence interval for B.

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