Give an interpretation to the term R-sq and comment on its value. (v) Perform the F test making sure to state the null and alternative hypotheses. (vi) State one limitation of using the regression equation for predicting the value of the TUITION charges.
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.
The following regression is fitted using variables identified that could be related to tuition charges ($) of a University.
TUITION = α + β ACCEPT + γ MSAT + λ VSAT
Where ACCEPT = the percentage of applicants that was accepted by the university, MSAT =
The data was processed using MNITAB and the following is an extract of the output obtained:
The regression equation is
TUITION = (deleted)
Predictor Coef StDev T P
Constant -26780 6115 -4.38 0.000
ACCEPT 116.00 37.17 * 0.003
MSAT -4.21 14.12 -0.30 0.767
VSAT 70.85 15.77 4.49 0.000
S = 2685 R-Sq = 69.6% R-Sq(adj) = 67.7%
Analysis of Variance
Source DF SS MS F P
Regression 3 808139371 269379790 37.37 0.000
Residual Error 49 353193051 7208021
Total 52 1161332421
(iv) Give an interpretation to the term R-sq and comment on its value.
(v) Perform the F test making sure to state the null and alternative hypotheses.
(vi) State one limitation of using the regression equation for predicting the value of the TUITION charges.
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