Question

For the table that follows, answer the following questions:

x y
1 1/2
2 1
3 3/2
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?

Answer 1

Take
m1=(y(2)-y(1))/(2-1)=0.5
m2=(y(3)-y(2))/(3-2)=0.5
Since the slopes between any of the three points equal 0.5, so the first three points are collinear, and m1=m2>0 so the slope is positive.

Can you take it from here?

Answer 2

This is so confusing to me :( what would i do next??

Answer 3

If you wish, you can calculate the coefficient of correlation according to the method you use at school (mayer, median/median, etc.) using the first three pairs of data.

In the given case, the coefficient of correlation should be 1.0 because the first three points are collinear (fall on a straight line). The slope is positive (0.5), so the answer to the fourth question is positive.

I will let you calculate the coefficient of correlation (and confirm that it is 1.0).