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# Linear Regression: Non-insect Relative Abundance vs. Percent Sands and Fines for Minnesota Streams

## Plot

1. Analysis: Linear regression
2. Independent variable: Percent (%) sand and fines
3. Dependent variable: Non-insect abundance/m²
4. Classification: Using Omernik level II Ecoregions with dummy variable = 0 for Ecoregions 46, 47, and 51 and dummy variable = 1 for Ecoregions 50 and 52.
5. Key: symbols = observations, solid line = mean line, dashed line = 95% prediction limit, black lines and symbols = Ecoregions 46, 47 and 51, blue lines and symbols = Ecoregions 50 and 52
6. Sample size: n = 267

## Model

1. Ecoregions 50 and 52: loge(Non-insect Abundance + 1) = 3.191 - 0.00375*(% sand & fines)
2. Ecoregions 46, 47 and 51: loge(Non-insect Abundance + 1) = 3.909 - 0.00651*(% sand & fines)
3. r² = 0.159
4. Date: 6 October, 2006
Variable Estimate t value p
Intercept  3.909 19.05
Ecoregion class -0.718 -2.71 0.007
% Sand & fines 0.00651 2.08 0.038
% Sand & fines x Ecoregion class -0.00276 -0.57 0.57

## Data Analysis

1. Non-insect abundance was transformed by taking the natural log of abundance +1 for each observation.
2. Model generated using SAS Proc GLM with the solution option. The 95% prediction limits were calculated using the equation in step 9 of box 14.3 from Sokal and Rohlf (1995). The intercept, slope, grand mean of % sand & fines, and corrected sums of squares were calculated using Proc REG and Proc UNIVARIATE.
3. The ecoregions were aggregated into two classes because a preliminary ANOVA indicated that the base material for bedded sediments, % coarse substrates, was significantly greater in Ecoregions 50 and 52 than in Ecoregions 46, 47, and 51. Percent coarse substrates, however, did not significantly differ within either group.
4. Replicate visits to a site were excluded from the data set.

## Data Origin

1. Agency: Minnesota Pollution Control Agency, St. Paul, Minnesota Exit
2. Location: Minnesota - analyses restricted to wadeable sites (52 km² < watershed area < 523 km²) from the five ecoregions indicated below.
3. Omernik Level III Ecoregions examined include: 46 (Northern Glaciated Plains), 47 (Western Corn Belt Plains), 50 (Northern Lakes and Forests), 51 (North Central Hardwoods), and 52 (Driftless Area).

## Sampling Design

1. Data collected 1996 through 2004.