Statistical Models
Interpolation and extrapolation

Statistical Models

Bivariate Statistics

• The statistical investigation process
• Association between variables
• The effects of outliers on correlation
• Causality
• Interpreting Pearson's correlation coefficient
• Calculating linear regression {TI-84 Plus CE}
• Interpreting values of linear regression
• Residual plots {TI-84 Plus CE}
• Calculating exponential regression {TI-84 Plus CE}
• Interpreting values of exponential regression
• ​Interpolation and extrapolation​

The Normal Distribution

• Properties of the bell shape curve
• Finding integral and non-integral probabilities {TI-84 Plus CE}
• Finding quantiles {TI-84 Plus CE}​

When a scatterplot is created between two variables, we describe the highest and lowest x-variables as the upper and lower poles respectively. If a line of best fit has been drawn, then predictions can be made for one variable given the other.

• If we predict a value that occurs in between the lower and upper poles, then we say we are interpolating between the poles.
• If we predict a value that occurs outside of either the lower or upper pole, then we say we are extrapolatingoutside the poles.

The accuracy of the predictions in either situation depends on how strong the correlation of the original data was to begin with. However, the extrapolation of data assumes that the correlation is going to continue outside of the poles. The validity of this assumption depends greatly on the situation we are looking at.