The data set represents the correlation between student's GPA and ACT scores. GPA is the explanatory variable and ACT is the response variable. There is a positive correlation between GPA and ACT scores. The correlation coefficient is .9821. This is close to one, so there is a strong linear correlation.
The least squares regression line is 6.789219x + 7.0670877. When I entered in a predicted value [yhat] of a GPA of 3.48 into the equation [6.789219*3.48 + 7.0670877] I got a predicted value of 30.694. The actual value the student received on the ACT was a 31. This means that my residual value is 0.36. The recorded value is above average.
The coefficient of determination is .9628. So, 96.28% of the variation in ACT scores is explained by the least squares regression line. This means that 96.28% of the variation in ACT scores is explained by the student's GPA. This leaves 3.72% of ACT score variation explained by other information.
The residual plot leaves no discernable pattern so this indicates that a linear model is appropriate for this data set analysis. The Box Plot of Residuals only shows one outlier, but it does not have much effect on the least squares regression line.


Simple linear regression results:
Dependent Variable: ACT Independent Variable: GPA ACT = 7.0670877 + 6.789219 GPA Sample size: 8 R (correlation coefficient) = 0.9812 Rsq = 0.96281034 Estimate of error standard deviation: 1.4014564 Parameter estimates:
Analysis of variance table for regression model:


Correlation between ACT and GPA is:
0.981229 
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Oct 29, 2009
Nice work!