#### Question You Asked

How much spatial clustering is present in the regression model of vegetation response to canopy cover? I am interested in determining if a single equation can predict the way that the two variables interact within east-side ponderosa pine forests, or if multiple equations are necessary.

#### Name of Tool or Approach You Used

To answer this question, I used the Geographically Weighted Regression tool in ArcMap.

#### Brief description of steps you followed to complete the analysis

In the GWR tool, I used vegetation cover as the dependent variable, and canopy cover as the explanatory variable. Because my points are somewhat clustered across the landscape, I used an adaptive kernel with an AICc bandwidth method.

#### Brief description of results you obtained

The map of coefficients did reveal certain clusters of high coefficients and low coefficients across the landscape. However, judging by the GWR table below, this clustering may not be statistically significant. One anomaly of this assessment was the negative adjusted R^{2} value. A negative R^{2} means that the equation did not include a constant term.

Map of clustered plots

VARNAME | VARIABLE | DEFINITION |

Neighbors | 46 | |

ResidualSquares | 14750.95231 | |

EffectiveNumber | 3.80525057 | |

Sigma | 18.69738296 | |

AICc | 405.3014401 | |

R2 | 0.048524493 | |

R2Adjusted | -0.01473284 | |

Dependent Field | 0 | Total_cvr |

Explanatory Field | 1 | Canopy_Cov |

*Table of original GWR results*

To remedy the negative adjusted R^{2}, I tried adding in another explanatory variable (elevation). This appeared to help the model, reducing the residual squares and bringing the adjusted R^{2} value back above 0.

VARNAME | VARIABLE | DEFINITION |

Neighbors | 46 | |

ResidualSquares | 13904.07263 | |

EffectiveNumber | 5.22764912 | |

Sigma | 18.46665082 | |

AICc | 405.8795404 | |

R2 | 0.103150476 | |

R2Adjusted | 0.01015694 | |

Dependent Field | 0 | Total_cvr |

Explanatory Field | 1 | Canopy_Cov |

Explanatory Field | 2 | Elevation |

*Table of remedied GWR*

#### Critique of the method – what was useful, what was not?

This method was useful in that I could process the data in ArcMap, which is where I was already analyzing my points. It was also very helpful to visualize the coefficients in the map below. However, I am still a little unsure why the coefficient map shows such strong clustering while the output table does not show any significance.