For the table that follows, answer the following questions:

x y
1 -8
2 -11
3 -14
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?

Positive correlation means both variables increase/decrease together. Negative correlation means one variable increases while the other decreases.

What is the consistent difference between the y values to determine the missing value?

How good is the predictability of y from x?

Slope value (±) is the same as the correlation value (±).

To find the answers to these questions, let's analyze the given table step-by-step:

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 observe the pattern in their relationship. Looking at the given table, as the value of x increases, the value of y decreases consistently. This means that as x increases, y decreases, indicating a negative correlation between x and y.

2. Find the missing value of y in the table.
To find the missing value of y in the table, we can observe the pattern between x and y. Based on the given table, the difference between consecutive x-values is always 1, and the difference between consecutive y-values is always 3. Applying this pattern, the missing value of y can be found by subtracting 3 from the previous y-value:

y (missing) = y (previous) - 3
Since the previous y-value is -14, we can calculate the missing value:
y (missing) = -14 - 3 = -17

So, the missing value of y in the table is -17.

3. How would the values of this table be interpreted in terms of linear regression?
In terms of linear regression, the values of the table represent a negative linear relationship between x and y. As x increases by 1 unit, y decreases by 3 units. This implies that there is a consistent decrease in the value of y for each unit increase in x.

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 we have determined that there is a negative correlation between x and y, the slope of the line of best fit placed among these points would also be negative. The line would have a downward slope from left to right, indicating a decrease in y as x increases.