Term
| 1. Requirement for inference on the least-squares regression model |
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Definition
The population is linear on x
mew (ylx) = B1x + B0 |
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Term
| 2. Requirement for inference on the least-squares regression model |
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Definition
| The response variables are normally distributed with mean mew (ylx) = B1x + B0 |
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Term
| Least-squares regression model |
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Definition
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Term
| Standard error of the estimate |
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Definition
| The unbiased estimator of sigma |
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Term
| Standard error of the estimate, se = |
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Definition
| [(summation(yi-yihat)^2)/n-2]^0.5 |
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Term
| The denominator of the standard error of the estimate is |
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Definition
| n-2 because 2 parameters (betas) cause it to lose 2 degrees of freedom |
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Term
| Because the response variable needs to be normally distributed for a least-squares regression, this means that |
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Definition
| ei, the residuals, must also be normally distributed |
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Term
| If there is no linear relationship between the response and explanatory variables, the slope of the true regression line will be |
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Definition
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Term
| Two-tailed test, least-squares regression |
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Definition
| Testing whether a linear relation exists between two variables without regard to the slope |
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Term
| Left-tailed test, least-squares regression |
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Definition
| Testing whether the slope of the true regression line is negative |
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Term
| Right-tailed test, least-squares regression |
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Definition
| Testing whether the slope of the true regression line is positive |
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Term
| Least-squares regression model, t-distribution = |
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Definition
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Term
| Least-squares regression model, sb1 = |
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Definition
| [se/(summation(xi-xbar)^2)^0.5] |
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Term
| 2 requirements for hypothesis test regarding the slope coefficient, B1 |
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Definition
1. The sample is obtained using random sampling
2. The residuals are normally distributed with constant error variance |
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Term
Two-tailed test, slope coefficient
H0: p =
H1: p = |
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Definition
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Term
Left-tailed test, slope coefficient
H0: p =
H1: p = |
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Definition
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Term
Right-tailed test, slope coefficient
H0: p =
H1: p = |
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Definition
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Term
Two-tailed test, classical approach
If t0 > t(alpha/2) |
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Definition
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Term
Left-tailed test, classical approach
If t0 < -t(alpha) |
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Definition
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Term
Right-tailed test, classical approach
If t0 > t(alpha) |
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Definition
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Term
P-value approach
If p-value < alpha |
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Definition
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Term
| The slope coefficient hypothesis testing is considered |
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Definition
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Term
| The confidence interval for the slope of the least-squares regression line is of the form |
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Definition
| Point estimate +/- margin of error |
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Term
| Lower bound CI, slope of the regression line = |
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Definition
| b1 - t(alpha/2)[se/(summation(xi-xbar)^2)] |
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Term
| Upper bound CI, slope of the regression line = |
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Definition
| b1 + t(alpha/2)[se/(summation(xi-xbar)^2)] |
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Term
| Bivariate normal distribution/Jointly normal distributed |
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Definition
| When the y's at any given x and the x's at any given y are normally distributed |
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