26- It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. The interpretation of the coefficient of determination in this regression is Regressing GPA on ACT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.7598 0.5774 0.5069 0.2691 Observations ANOVA df SS Significance F 0 0286 MS F Regression Residual 0.5940 0.5940 8.1986 0.4347 0.0724 Total 1.0287 Coefficients Standard Error 0.5681 t Stat P-value Upper 95% 2.8398 Lower 95% Intercept 0.9284 0.6119 0.5630 -1.7036 ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 a) GPA accounts for 57.74% of the variability of ACT scores. b) 57.74% of the total variation of ACT scores can be explained by GPA. C) None of the given statements. d) ACT Scores account for 57.74% of the total fluctuation in GPA. 167

26- It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. The interpretation of the coefficient of determination in this regression is Regressing GPA on ACT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.7598 0.5774 0.5069 0.2691 Observations ANOVA df SS Significance F 0 0286 MS F Regression Residual 0.5940 0.5940 8.1986 0.4347 0.0724 Total 1.0287 Coefficients Standard Error 0.5681 t Stat P-value Upper 95% 2.8398 Lower 95% Intercept 0.9284 0.6119 0.5630 -1.7036 ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 a) GPA accounts for 57.74% of the variability of ACT scores. b) 57.74% of the total variation of ACT scores can be explained by GPA. C) None of the given statements. d) ACT Scores account for 57.74% of the total fluctuation in GPA. 167

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

26 - It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship
with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly
chosen students from a Big-Ten university.
The interpretation of the coefficient of determination in this regression is
Regressing GPA on ACT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0.7598
0.5774
0.5069
0.2691
Observations
ANOVA
df
SS
Significance F
0 0286
MS
F
Regression
Residual
0.5940
0.5940
8.1986
6.
0.4347
0.0724
Total
1.0287
Coefficients Standard Error
t Stat
Upper 95%
2.8398
P-value
Lower 95%
Intercept
0.5681
0.9284
0.6119
0.5630
-1.7036
ACT
0.1021
0.0356
2.8633
0.0286
0.0148
0.1895
a)
GPA accounts for 57.74% of the variability of ACT scores.
b)
57.74% of the total variation of ACT scores can be explained by GPA.
C)
None of the given statements.
d) ACT Scores account for 57.74% of the total fluctuation in GPA.

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