Question 478486: For the table that follows, answer the following questions:
x------y
1------5
2------7
3------9
4------
- Would the correlation between x and y in the table above be positive or negative?
- Find the missing value of y in the table.
- How would the values of this table be interpreted in terms of linear regression?
- If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! For the table that follows, answer the following questions:
x------y
1------5
2------7
3------9
4------x
-----
Would the correlation between x and y in the table above be positive or negative?
THE CORRELATION WOULD BE POSITIVE
-----
Find the missing value of y in the table.
THE MISSING VALUE IS 11
FOR EVERY INCREASE OF 1 IN THE VALUE OF X, YOU ARE GETTING AN INCREASE OF 2 IN THE VALUE OF Y.
THE EQUATION DERIVED FROM THIS DATA WOULD BE Y = 2X + 3
IF YOUR SEQUENCE OF X VALUES WAS 0,1,2,3,4,5, THEN YOUR SEQUENCE OF Y VALUES WOULD BE 3,5,7,9,11,13
THE SLOPE OF THE LINE Y = 2X + 3 IS EQUAL TO 2 WHICH MEANS THAT THE CHANGE IN Y DIVIDED BY THE CHANGE IN X IS EQUAL TO 2.
FOR EVERY CHANGE OF 1 IN THE VALUE OF X, YOU ARE GETTING A CHANGE OF 2 IN THE VALUE OF Y.
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How would the values of this table be interpreted in terms of linear regression?
YOU WOULD USE THE CORRELATION FORMULA TO DETERMINE WHAT THE CORRELATION IS.
YOU WOULD USE THE LINEAR REGRESSION FORMULA TO DETERMINE THE STRAIGHT LINE THAT BEST FITS THE DATA
IT LOOKS TO ME THAT YOU CORRELATION WOULD BE 100% BECAUSE EVERY POINT WOULD FIT ON THE LINE.
THE LINEAR REGRESSION LINE LOOKS LIKE IT WILL BE Y = 2X + 3
A GRAPH OF THAT EQUATION IS SHOWN BELOW:
those horizontal lines are at y = 5,7,9
those vertical lines are at x = 1,2,3
the intersection of the horizontal lines with the vertical lines with the equation of the line tell you the value of y for that value of x.
when x = 1, y = 5
when x = 2,y = 7
when x = 3, y = 9
the vertical lines are difficult to draw using the algebra.com graph generator software, but they're close enough for you to get the idea.
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If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?
THE SLOPE OF THE LINE WOULD BE POSITIVE
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here's a reference that helps explain how it's done.
http://people.hofstra.edu/Stefan_Waner/RealWorld/calctopic1/regression.html
here's a reference that does the calculations for you.
http://www.alcula.com/calculators/statistics/linear-regression/
easiest way to enter the data is first line is all x values and second line is all corresponding y values.
it needs at least 5 sets of data pairs, so you'll need to extrapolate from your problem to enter data as:
1 2 3 4 5
5 7 9 11 12
it will generate the graph for you after you click on submit plot and will show you the actual data plot or the correlation plot by just clicking on the appropriate button.
it's real easy to use and a good learning tool.
here's another reference that might be easier to use the discusses the formulas used and how to solve the problem with them.
http://easycalculation.com/statistics/learn-regression.php
http://easycalculation.com/statistics/learn-correlation.php
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