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Significance of the Residual Plot

Conclusion

The residual plot shows that despite having a weak correlation coefficient, the line is still appropriate for the data because all the residual points are scattered randomly above and below the line and doesn't show a pattern such as a U-curve.

From the data that I have collected, and through the use of using linear regression, I reject my original hypothesis because while there is a correlation between height and intelligence, the linear square regression line or LSRL's equation and values reveals that the relation is negative and weak. And so I can only conclude that height alone does not contribute to students or anyone else who possess high levels of intelligence. Other factors can include the environment that people are raised in such as location, discipline, access to education, and maybe even the amount of money that a person possesses. So in conclusion, there is a negative and weak relation between height and intelligence.

A Relation between Height and Intelligence?

Done by Callie Griffin

What's it all mean?

For the slope it means that for every inch taller a person is, PIQ scores drop by 0.3319. While for the Y intercept, it means that at the height of 0 inches, a person's PIQ score is supposed to be 134.44. The correlation coefficient value of -.05 means that the line is in a negative direction and is weak in strength. The coefficient of determination of 0.003 means that 0.003% of the variation in PIQ is accounted for by the linear relationship between height and PIQ.

Residual Plot

This is the residual plot for the data where x is height, and y is the residual.

Scatter plot

Values of the Scatter Plot and Line

My Hypothesis

For this project, I've decided to do it on what I believe is one of science's greatest mysteries. That question: is there a relation between a person's height and intelligence? I hypothesis that the line for height and intelligence would have a positive correlation with moderate strength (between 0.5 and 0.8) with the explanatory value x in height (that is in inches) and the response value y in Performance IQ (PIQ for short).

Equation of the Line: Y= -0.3319x + 134.44

The slope is -0.3319

The Y-intercept is 134.44

The correlation coefficient is -0.05

The coefficient of determination is 0.003

There are no outliers present

The following data was taken from a survey in which 38 students answered their height and their PIQ. The results are shown in the scatter plot above.

Data courtesy of: http://sites.stat.psu.edu/~lsimon/stat501wc/sp05/data/iqsize.txt

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