AP Linear Regression Test - Expectations
1) Know how to use TI-83 to get equation of least-squares regression line, to calculate correlation (r), and to calculate the coefficient of determination (r^2). Also, know how to create a scatterplot, scatterplot with fitted least-squares regression line, and residual plot.
2. Know how to use the AP Formula sheet - specifically know how to determine the formula for the least squares regression line given summary statistics (r, Sx, Sy, etc.)
3) Know how to calculate residuals.
4) Know the following properties of correlation:
A) The correlation coefficient does not change with changes to measurements of scale. That is, if the height is expressed in meters or feet, the correlation coefficient does not change.
B) r falls between -1 and +1
C) Correlation only measures the strength and direction of a linear relationship. A non-linear relationship can exist and the correlation could be close to 0.
D) Correlation measures the strength and direction of a linear relationship.
E) If correlation is negative, slope must be negative. If correlation is positive, slope must be positive.
5) ***Be able to state the equation of a least-squares regression line and interpret its slope in the context of the question/problem. For example, if we refer to the relationship between girth (the explanatory variable) and volume (the response variable) found in the trees dataset. We can conclude that the slope is 5.06. Therefore, we can state:
The slope of 5.06 indicates that for every 1 inch increase in girth, there will be an average increase in volume of 5.06 cubic feet.
Be able to interpret the coefficient of determination in the context of the problem. For example, with the the trees dataset from above - the coefficient of determination - r squared (r^2) was calculated to be 0.935. Therefore we can state:
The regression output indicates that r^2 = 0.935. Thus, 93.5% of the variation in volume values is explained by using the linear regression model with the girth of the trees as the explanatory variable.
6) Know that the mean of the residuals = 0.
7) Know that (x-bar, y-bar) falls on the least-squares regression line.
8) Know how to tell if a residual plot is good or not.
9) Know that for a given set of data, the least-squares regression line is the 1 line that minimizes the sum of the residuals squared.
2. Know how to use the AP Formula sheet - specifically know how to determine the formula for the least squares regression line given summary statistics (r, Sx, Sy, etc.)
3) Know how to calculate residuals.
4) Know the following properties of correlation:
A) The correlation coefficient does not change with changes to measurements of scale. That is, if the height is expressed in meters or feet, the correlation coefficient does not change.
B) r falls between -1 and +1
C) Correlation only measures the strength and direction of a linear relationship. A non-linear relationship can exist and the correlation could be close to 0.
D) Correlation measures the strength and direction of a linear relationship.
E) If correlation is negative, slope must be negative. If correlation is positive, slope must be positive.
5) ***Be able to state the equation of a least-squares regression line and interpret its slope in the context of the question/problem. For example, if we refer to the relationship between girth (the explanatory variable) and volume (the response variable) found in the trees dataset. We can conclude that the slope is 5.06. Therefore, we can state:
The slope of 5.06 indicates that for every 1 inch increase in girth, there will be an average increase in volume of 5.06 cubic feet.
Be able to interpret the coefficient of determination in the context of the problem. For example, with the the trees dataset from above - the coefficient of determination - r squared (r^2) was calculated to be 0.935. Therefore we can state:
The regression output indicates that r^2 = 0.935. Thus, 93.5% of the variation in volume values is explained by using the linear regression model with the girth of the trees as the explanatory variable.
6) Know that the mean of the residuals = 0.
7) Know that (x-bar, y-bar) falls on the least-squares regression line.
8) Know how to tell if a residual plot is good or not.
9) Know that for a given set of data, the least-squares regression line is the 1 line that minimizes the sum of the residuals squared.