Predicting final exams How well do exams given duringthe semester predict performance on the final? One classhad three tests during the semester. Computer output ofthe regression givesDependent variable is Finals = 13.46 R-Sq = 77.7, R-Sq(adj) = 74.1,Predictor Coeff SE(Coeff) t-Ratio P-ValueIntercept -6.72 14.00 -0.48 0.636Test1 0.2560 0.2274 1.13 0.274Test2 0.3912 0.2198 1.78 0.091Test3 0.9015 0.2086 4.32 60.0001Analysis of VarianceSource DF SS MS F-Ratio P-ValueRegression 3 11961.8 3987.3 22.02 60.0001Error 19 3440.8 181.1Total 22 15402.6a) Write the equation of the regression model.b) How much of the variation in final exam scores isaccounted for by the regression model?c) Explain in context what the coefficient of Test3 scoresmeans.d) A student argues that clearly the first exam doesn’t helpto predict final performance. She suggests that this examnot be given at all. Does Test1 have no effect on the finalexam score? Can you tell from this model? (Hint: Doyou think test scores are related to each other?)
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.
Predicting final exams How well do exams given during
the semester predict performance on the final? One class
had three tests during the semester. Computer output of
the regression gives
Dependent variable is Final
s = 13.46 R-Sq = 77.7, R-Sq(adj) = 74.1,
Predictor Coeff SE(Coeff) t-Ratio P-Value
Intercept -6.72 14.00 -0.48 0.636
Test1 0.2560 0.2274 1.13 0.274
Test2 0.3912 0.2198 1.78 0.091
Test3 0.9015 0.2086 4.32 60.0001
Analysis of Variance
Source DF SS MS F-Ratio P-Value
Regression 3 11961.8 3987.3 22.02 60.0001
Error 19 3440.8 181.1
Total 22 15402.6
a) Write the equation of the regression model.
b) How much of the variation in final exam scores is
accounted for by the regression model?
c) Explain in context what the coefficient of Test3 scores
means.
d) A student argues that clearly the first exam doesn’t help
to predict final performance. She suggests that this exam
not be given at all. Does Test1 have no effect on the final
exam score? Can you tell from this model? (Hint: Do
you think test scores are related to each other?)
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