Flashcards in BIO 330 Deck (379)

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241

## extrapolating linear regression

### DO NOT extrapolate beyond data, can't assume relationship continues to be linear

242

## linear regression Ho

### Slope is zero (β = 0), number of dees cannot be predicted from predator mass

243

## linear regression Ha

### slope is not zero (β ≠ 0), number of dees can be predicted from predator mass (2 sided)

244

## Hypothesis testing of linear regression

###
testing about the slope:

–t-test approach

–ANOVA approac

245

## Putting linear regression into words

###
Dee rate = 3.4 - 1.04(predator mass)

Number of dees decreases by about 1 pre kilo of predator mass increase

246

## testing about the slope, t-test approach

###
test statistic t = b–β_o / SE_b

SE_b = √MSresidual/Σ(Xi-Xbar)^2

MSres. = Σ(Yi-Yhat)^2 / n-2

critical t = t_α(2),df

df = n - 2

compare statistic, critical

247

## testing about the slope, ANOVA approach

###
source of variation: regression, residual, total

sum of squares, df, mean squares, F-ratio

248

## calculating testing about the slope, ANOVA approach

###
SSregres = Σ(Yi^ - Ybar)^2

SSresid. = Σ(Yi-Yi^)^2

MSreg. = SSreg/df df=1

MSresid = SSres/df df=n-2

F-ratio = MSreg/MSres.

SStotal = Σ(Yi-Ybar)^2

df total = n-1

249

## interpreting ANOVA approach to linear regression

### If Ho is true, MSreg. = MSres

250

## % of variation in Y explained by X

###
R^2 = SSreg/SStotal

a% of variation in Y can be predicted by X

251

## Outliers, linear regression

### create non-nomral Y-value distribution, violate assumption of equal variance in Y, strong effect on slope and intercept; try not to transform data

252

## linear regression assumptions

###
linear relationship

normality of Y at each X

variance of Y same for every X

random sampling of Y's

253

## detecting non-linearity

### look at the scatter plot, look at residual plot

254

## checking residuals

###
should be symmetric above/below zero

should be more points close line (0) than far

equal variance at all values of x

255

## non-linear regression

### when relationship is not linear, transformations don't work, many options- aim for simplicity

256

## quadratic curves

###
Y = a + bX + cX^2

when c is negative, curve is humped

when c is positive, curve is u shaped

257

## multiple explanatory variables

###
improve detection of treatment effects

investigate effects of ≥2 treatments + interactions

adjust for confounding variables when comparing ≥2 groups

258

## GLM

### general linear model; multiple explanatory variables can be included (even categorical); response variable (Y) = linear model + error

259

## least-squares regression GLM

###
Y = a + bX

error = residuals

260

## single-factor ANOVA GLM

###
Y = µ + A

error = variability within groups

µ = grand mean

261

## GLM hypotheses

###
Ho: response = constant; response is same among treatments

Ha: response = constant + explanatory variable

262

## constant

### constant = intercept or grand mean

263

## variable

### variable = variable x coefficient

264

## ANOVA results, GLM

###
source of variation: Companion, Residual, Total

SS, df, MS, F, P

265

## ANOVA, GLM F-ratio

### MScomp. / MSres.

266

## ANOVA, GLM R^2

###
R^2 = SScom. / SStot.

% of variation that is explained

267

## ANOVA, GLM, reject Ho

### Model with treatment variable fits the data better than the null model but only 25% of the variation is explained

268

## Multiple explanatory variables, goals

###
improve detection of treatment effects

adjust for effects of confounding variables

investigate multiple variables and their interaction

269

## design feature for improving detection of treatment effects

### blocking

270