Chapter 8 Summary
Key Concepts Summary
- 8.1 Linear Correlation
- Calculating the linear correlation coefficients for any given sets and using it to determine stong/weak positive/negative or no correlation between the sets
- 8.2 Linear Regression
- Calculating a line of best fit for correlated variables using linear regression.
- Calculating the Coefficient of determination
Glossary of Terms
Bivariate Data. Two variables measured on each subject.
Correlation. The statistical association between two variables
Line of Best Fit. The balancing of the differences between the observed data to create a linear model that can be used to estimate new data points.
Predictor Variable. A random variable chosen to predict the changes in another variable.
Residual. The difference between the data predicted by the line of best fit and the actual observed data.
Response Variable. The random variable that is expected to change in response to changes in the predictor variable.
Formula & Symbol Hub
Symbols Used
- [latex]\bar{x}[/latex] = mean of set x
- [latex]S_x[/latex] = standard deviation of set x
- [latex]r[/latex] = linear correlation coefficient
- latex]b_0[/latex] = the y intercept of a line
- [latex]b_1[/latex] = the slope of a line
- [latex]x[/latex] = the predictor variable in linear regression
- [latex]\hat{y}[/latex] = the estimate of the mean in linear regression
Formulas Used
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Formula 8.1 – Linear Correlation Coefficient
[latex]\begin{align*}r=\frac{\sum\frac{\left(x_i-\bar{x}\right)}{S_x}\frac{\left(y_i-\bar{y}\right)}{S_y}}{n-1}\end{align*}[/latex]
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Formula 8.2 – Simple Linear Regression
[latex]\hat{y}=b_0+b_1x[/latex]
