Flashcards
BIOL 315 Flashcards 6
Cards in this deck (32)
- 1Objectives of Linear Regression1. Estimation of the line of best fit
2. Hypothesis Testing - 2Types of Hypothesis Testing Linear Regression1. t-test on the slope
2. Partitioning variance (ANOVA approach) - 3Linear RegressionA straight line relationship between continuous variables that gives a statistical description about X and Y variables in a sample
- 4X VariableThe explanatory variable, independent
- 5Y VariableThe response variable, dependent
- 6General Linear ModelUsed in regression analysis to give a statistical linear description and allows us to predict Yi from Xi
- 7ß1Slope of the Regression Line, a true population parameter that needs to be estimated (estimate is b1)
- 8ß0Intercept of the Regression Line, a true population parameter that needs to be estimated (estimate is b0)
- 9Estimates of Slope and InterceptThe estimates for slope and intercept are values that result in a line that passes as close to the sample data as possible
This line is known as the linear regression of Y on X - 10Hypothesed For Linear RegressionNull: the true slope is zero (ß1=0)
Alternative: the true slope is not zero (ß≠0) - 11Single-Sample t-Test on the SlopeOne method of hypothesis testing for linear regression. Uses a single sample t-test as usual, needs the MSerror where degrees of freedom are N—2
- 12ANOVA ApproachOne method of hypothesis testing for linear regression. Partitions the variance as in ANOVA: into SSr and SSe, then calculates the F-ratio as the test statistic
- 13SS(R)Sum of Squares Regression, equivalent to SSgroup in ANOVA
- 14SS(E)Sum of Squares Error, same as in ANOVA
- 15SS(XY)Sum of Cross Products or just Sum of Squares Products. Measures how deviations in X and Y vary together
- 16Coefficient of DeterminationUsed after the ANOVA approach in GLM regression to measure the relationship between X and Y, takes on a value between zero and one
- 17Assumptions of Linear Regression1. The residuals are independent of one another
2. The residuals are normally distributed with a mean of zero
3. The residuals have constant variance (homoscedasticity)
4. The relationship between X and Y is truly linear
5. X is measured without sampling error - 18Correlation AnalysisUsed when we want to know how 2 variables are related, when the variables are not assigned as dependent or independent
It is a statistical technique for measuring the association between 2 numerical variables known as Y1 and Y2 - 19Bivariate Normal DistributionThe joint probability distribution of 2 normally distributed variables
The population parameters that describe it are:
-mean and variance of Y1
-mean and variance of Y2
-value of rho - 20RhoThe population coefficient of correlation that measures the strength and direction of association between 2 variables, it is a true population parameter that is estimated by (r)
- 21True Population ParameterAre unknown, need to do estimates of them in calculations
- 22Pearson Correlation CoefficientAn estimate of rho that has a value between -1 and 1 where values close to ±1 indicate a correlation
- 23Hypotheses for Single Sample t-Test CorrelationNull: there is no association between Y1 and Y2
Alternative: there is an association between Y1 and Y2 - 24Assumptions for Correlation1. Each pair of observations is independent
2. Y1 and Y2 follow bivariate normal distributions
3. Y1 and Y2 demonstrate a linear relationship - 25Experimental StudyUse linear regression to determine on variable value from another in a causal relationship
- 26Observational StudyUse correlation analysis to determine patterns and associations between two variables
- 27AttenuationIncreased measurement error means r underestimates magnitude of rho. This means rho will be closer to zero than true correlation and is a bias called attenuation
- 28Least Squares RegressionProduces a line where sum of all squared deviations in Y is smallest
- 29ExtrapolationPredicting Y for X values beyond range of data
- 30ResidualsThe difference between the observed value of the dependent variable and the predicted value
- 31Confidence BandsUpper curve connects upper bounds of all 95% confidence intervals of predicted mean Y values, lower curve connects lower bounds of same confidence intervals
Together, upper and lower curves are called 95% confidence bands - 32Prediction IntervalsMeasure precision of the predicted single Y values for each X
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- Science (Bio 315) Flashcards on BIOL 315 Flashcards 6, created by Natasha Gidluck on 29/11/2020.
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