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.