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Created: Oct 20, 2009
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ACT vs. GPA

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 [y-hat] 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.

Result 1: Scatter Plot ACT vs. GPA   [Info]

Result 2: Boxplot Residuals ACT vs. GPA   [Info]

Result 3: Simple Linear Regression ACT vs. GPA   [Info]
Simple linear regression results:
Dependent Variable: ACT
Independent Variable: GPA
ACT = 7.0670877 + 6.789219 GPA
Sample size: 8
R (correlation coefficient) = 0.9812
R-sq = 0.96281034
Estimate of error standard deviation: 1.4014564
Parameter estimates:
 Parameter Estimate Std. Err. DF T-Stat P-Value Intercept 7.0670877 1.455576 6 4.855183 0.0028 Slope 6.789219 0.54473466 6 12.46335 <0.0001

Analysis of variance table for regression model:
 Source DF SS MS F-stat P-value Model 1 305.0905 305.0905 155.3351 <0.0001 Error 6 11.784478 1.9640797 Total 7 316.875

Result 4: Simple Linear Regression Fitted Line ACT vs. GPA   [Info]

Result 5: Correlation ACT vs. GA   [Info]
 Correlation between ACT and GPA is: 0.981229

Data set 1. ACT vs. GPA   [Info]