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?
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?
This is so confusing to me :( what would i do next??
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).
To find the answers to the questions, let's first take a look at the table:
x y
1 1/2
2 1
3 3/2
4 ?
Now let's answer each question one by one:
1. Would the correlation between x and y in the table above be positive or negative?
To determine the correlation between x and y, we need to analyze the pattern in the table. As we can see, when x increases, y also increases. This indicates a positive relationship between x and y. Therefore, the correlation between x and y in this table would be positive.
2. Find the missing value of y in the table.
Based on the pattern we observed, as x increases by 1, y increases by 1/2. Applying this pattern, we can calculate the missing value of y:
The value of y for x = 4 would be the value of y for x = 3 (3/2) plus 1/2:
y = 3/2 + 1/2 = 2
Hence, the missing value of y in the table is 2.
3. How would the values of this table be interpreted in terms of linear regression?
The values in this table can be interpreted as data points that represent a relationship between x and y. Since the relationship appears to be linear, we can use linear regression to find a line that best fits these data points.
4. 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?
Since the relationship between x and y is positive in this table, the line of best fit would have a positive slope. A positive slope means that as x increases, y also increases.