StatCrunch logo (home)

Report Properties

from Flickr
Created: Oct 20, 2009
Share: yes
Views: 17290
Results in this report
Data sets in this report
Need help?
To copy selected text, right click to Copy or choose the Copy option under your browser's Edit menu. Text copied in this manner can be pasted directly into most documents with formatting maintained.
To copy selected graphs, right click on the graph to Copy. When pasting into a document, make sure to paste the graph content rather than a link to the graph. For example, to paste in MS Word choose Edit > Paste Special, and select the Device Independent Bitmap option.
You can now also Mail results and reports. The email may contain a simple link to the StatCrunch site or the complete output with data and graphics attached. In addition to being a great way to deliver output to someone else, this is also a great way to save your own hard copy. To try it out, simply click on the Mail link.
Mail   Print   Twitter   Facebook

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]
Right click to copy

Result 2: Boxplot Residuals ACT vs. GPA   [Info]
Right click to copy

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]
Right click to copy

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

Data set 1. ACT vs. GPA   [Info]
To analyze this data, please sign in.

HTML link:
<A href="">ACT vs. GPA</A>

Want to comment? Subscribe
Already a member? Sign in.
Oct 29, 2009

Nice work!

Always Learning