Basic Theory

1. The best fitting line is found using advanced math to minimize the vertical distances from the points to the line. Hence, the Y coordinate of a point on the best fitting line provides an estimate of Y at the value of the corresponding X coordinate This process is called regression (to move backward) because ? The estimate of Y will be closer to the mean in standard deviations than X is. ? The estimate of Y will be farther from the mean in standard deviations than X is.

2. Highlight all assumptions requiring validation for linear regression and prediction ? Scatter plot pattern is reasonably straight (Linearity) ? No points lie far enough away to pull the line of best fit away from the main point pattern. ? The plot does not fan out as x increases or decreases (Equal Spread) ? Predict Y at a value of X within the range of the X data

3. The “intercept” and “slope” completely define the best fitting line. The intercept is the vertical distance from the origin (where the X and Y axes intersect) up to the line. It sets the elevation of the line ? TRUE ? FALSE

4. As the slope increases ? The line moves up ? The line moves down ? The line rotates clockwise ? The line rotates counterclockwise

5. R² measures the fit of the line to the points. As R²increases ? The scatter about the line increases and the amount of the variation of Y explained by X decreases ? The scatter about the line decreases and the amount of the variation of Y explained by X increases ? The scatter about the line increases and the amount of the variation of Y explained by X increases ? The scatter about the line decreases and the amount of the variation of Y explained by X decreases

6. The correlation R measures the linear dependence of Y on X, and does not have a unit of measure. ? True ? False

7. Highlight the 3 correct statements ? X denotes the independent or response variable ? X denotes the independent or explanatory variable ? Y denotes the dependent or explanatory variable ? Y denotes the dependent or response variable

? x denotes the observed value of the dependent variable ? denotes the mean value of observations of the response variable

ScholarMatic: Explanation & Answer

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