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Suppose you have two variables X and Y, and a set of paired values for them.
You can draw a line in the xy-plane: say y = ax + b. For each point, the residual is defined as the observed value y minus the fitted value: that is, the vertical distance between the observed and expected values.
The least squares regression line is the line which minimises the sum of the squares of all the residuals.
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What polygon has at least one pair of parallel line segments?
Many polygons, such as squares, rectangles, rhombi, parallelograms, etc. have more than 1 pairs of parallel line segments. Trapezoids have only 1 pair of parallel line segments. These few shapes are just quadrilaterals, other polygons also have more than 1 pair of parallel line segments (e.g. regularhexagons, octagons, etc.). Triangles never have any parallel line segments.
Do all parallelograms have at least one right angle?
The simple answer is no, not all parallelograms have at least one right angle. However, there are some that do. Rectangles and squares are 'special' parallelograms that all have at least one right angle.
How do you form two squares by drawing five lines?
Draw a rectangle with length twice its width, you would have used 4 lines already. Then draw a straight line at the center. The result will be two identical squares.
How many 3x3 squares are in a strip of squares that is 3 squares tall and 50 squares long?
There are 48 such squares.
Does quadrilaterals have least 1 line of symmetry?
No.
What is another name for the regression line?
It is often called the "Least Squares" line.
Is the least-squares regression line resistant?
No, it is not resistant.It can be pulled toward influential points.
Is the slope of the Least Squares Regression Line very sensitive to outliers in the x direction with large residuals?
Yes, it is.
Weighted Least Squares regression?
Yes, it does exist.
What negative correlation indicate?
the negative sign on correlation just means that the slope of the Least Squares Regression Line is negative.
Why are there two regression lines?
There are two regression lines if there are two variables - one line for the regression of the first variable on the second and another line for the regression of the second variable on the first. If there are n variables you can have n*(n-1) regression lines. With the least squares method, the first of two line focuses on the vertical distance between the points and the regression line whereas the second focuses on the horizontal distances.
If the regression sum of squares is large relative to the error sum of squares is the regression equation useful for making predictions?
If the regression sum of squares is the explained sum of squares. That is, the sum of squares generated by the regression line. Then you would want the regression sum of squares to be as big as possible since, then the regression line would explain the dispersion of the data well. Alternatively, use the R^2 ratio, which is the ratio of the explained sum of squares to the total sum of squares. (which ranges from 0 to 1) and hence a large number (0.9) would be preferred to (0.2).
What should you use to find the equation for a line of fit for a scatter plot?
Least squares regression is one of several statistical techniques that could be applied.
What is the slope b of the least squares regression line y equals a plus bx for these data?
The graph and accompanying table shown here display 12 observations of a pair of variables (x, y).The variables x and y are positively correlated, with a correlation coefficient of r = 0.97.What is the slope, b, of the least squares regression line, y = a + bx, for these data? Round your answer to the nearest hundredth.2.04 - 2.05
What has the author Naihua Duan written?
Naihua Duan has written: 'The adjoint projection pursuit regression' -- subject(s): Least squares, Regression analysis
What is a least square regression line?
If you plot data points on a graph the rarely will form a straight line. Least squares is a method of finding a line 'close' to all the data points instead of just guessing and drawing a line that looks good. If you have a line, then there is an algebraic formula to find the distance from each point to that line. Then using statistics, you can make the statistically averaged distance from each data point as close as possible to a line. The distances are squared, averaged, and the average of those squared distances may be used to find the regression line.
What characteristic makes regression line of best fit?
The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.
