Term
| Analysis of Variance (ANOVA) |
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Definition
| compare multiple means from multiple populations |
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Term
| 2 types of variability for ANOVA tests are: |
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Definition
1) within the sample (random error)
2) between the samples (treatment error) |
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Term
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Definition
1) normality of the populations
2) homoscedasticity of the population variances
3) independence of the observations |
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Term
| If the MSA/MSE ratio is small, the P-value will be _______, and we would _____ Ho. |
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Definition
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Term
| When P is _____, ______ Ho. |
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Definition
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Term
| Familywise confidence interval |
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Definition
| interval containing all the u's. We'd use Turkey's test for this |
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Term
| Simple linear regression's 3 Types of Relationships: |
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Definition
1) No relationship (β1 = 0)
2) Positive (1 > β1 > 0)
3) Negative (0 > β1 > -1) |
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Term
| For the regression model, we wish to minimize ______. |
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Definition
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Term
| Assumptions for Regression Model (y = βo + β1*X + Ei): |
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Definition
1) Ei ~ N(0, σ^2)
2) Values of y must have equal variance across all values of x
3) Ei must be independently & identically distributed |
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Term
| The Coefficient of Determination (R^2) |
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Definition
-shows how well the regression line fits the data (we want it to be close to 1)
-R^2 = proportion of the total variability explained by x & y
-0 would indicate the line is not fit for the data
-we want R^2 to be at least .7 or greater generally |
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Term
| Checking Assumptions of ANOVA Test: |
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Definition
1) Check specifcity (if we're using the correct model) by creating a scatterplot
2) Check homostastity (if the variances of y are equal) by searching for heterostasticity with a residual plot. Heterostasticity is shown only is the data does not look like a horizontal line.
3) Test for independence by making sure there is no pattern to the data on the residual plot |
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Term
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Definition
-Checks all previous assumptions (except specifcity)
-Root mean square error is S
-Use a q-q plot of the residual to test normality |
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Term
| Prediction Intervals predict _______. |
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Definition
| future values of random variables |
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Term
| Confidence Intervals estimate _______. |
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Definition
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Term
| What effects the width of a confidence interval for Yo? |
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Definition
-Std. Deviation
-Sample Size
-The degrees of freedom
-How spread out the X's are (the more spread out the smaller the interval, aka if SSx is larger the width is smaller)
-How far Xo is from the center of the data (Xo - X bar) |
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Term
| Prediction Interval for Yo compared to Confidence Interval for Yo: |
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Definition
-Added source of variability because of random variable (specifically the added variability of the normal distribution)
-Prediction intervals will always be wider than the confidence interval |
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Term
| Correlation coefficient (e) |
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Definition
-measure of the linear association of two random variables
-NOT a measure of causality or prediction
-Just because there is no linear relationship, does not mean there isn't a relationship of another type |
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Term
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Definition
-an estimate of e
-gives the direction & strength of the linear relation |
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Term
| Assuming Ho is true, the statistics _____ and _____ both estimate the common popilation variance σ^2. |
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Definition
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Term
| A multiple comparison method in one factor ANOVA preserves the overall level of _____ that all ___________ simultaneously hold. |
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Definition
| confidence; confidence intervals |
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Term
| Purpose of a multiple-comparison method in ANOVA: |
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Definition
| to detect differences among population means and to estimate the differences in population means, provided differences exist. |
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Term
| There are _____ basic assumptions in simple linear regression analysis, which can be check. |
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Definition
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Term
| The population simple regression model is composed of: |
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Definition
| infinitely many homoscedastic normal distributions whose means compose a line in the form of E(Y) = βo + β1*X |
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Term
| Residual plots where the empirical residuals are plotted against the independent variable are used to check for: |
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Definition
| gross violations of the homoscedasticity assumption |
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