Question 664366: . For the table that follows, answer the following questions:
x y
1 1
2 4
3 7
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?
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! we will take two points and find equation of a line passing through
let points be ( ,), and ( , )
| Solved by pluggable solver: FIND EQUATION of straight line given 2 points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 1) and (x2, y2) = (3, 7).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(3)x + (-2)
Your graph:
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so, equation is:
 ....and the slope of this line is positive, 
now check if all points lie on same line:
as you can see, all points do lie on same line
now we can calculate  if  using :
 ..........the missing value
so, your table is:
x| y
1| 1
2| 4
3| 7
4| 10
now check if a point ( , ) also lie on a line
-correlation would be  % because every point fit on the line
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! for every increase of 1 in x, here is a corresponding increase of 3 in y.
this is a positive correlation.
the slope of the regression line would be equal to 3.
the slope of the regression line would be positive.
the missing value is y = 10 when x = 4.
the regression line equation would be y = 3x - 2
when x is equal to 1, y is equal to 3 * 1 - 2 = 3 - 2 = 1
when x is equal to 2, y is equal so 3 * 2 - 2 = 6 - 2 = 4
etc...
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