. For the table that follows, answer the following questions:
x y
1 -1
2 -5
3 -9
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. The missing value of y =
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?
Please show work!
hmmm. as x increases by 1, y decreases by 4.
That should make things clear.
To answer these questions, let's first plot the given points on a coordinate system.
Table:
x y
1 -1
2 -5
3 -9
4
Plotting these points gives us the following graph:
```
^
|
-10| o
| o
| o
-20|_________________________
1 2 3 4 5 6 7 x
```
Now let's address each question:
1. Would the correlation between x and y in the table above be positive or negative?
To determine the correlation, we need to analyze the relationship between x and y. Looking at the points, as x increases, y decreases. This indicates a negative correlation between x and y.
2. Find the missing value of y in the table. The missing value of y = ?
From the graph, we can see that when x is 4, y is also missing. However, we can observe a pattern in the y-values: each y-value is 4 less than the previous one. So, when x is 4, we can deduce that y would be -13 (since the previous y-value was -9).
3. How would the values of this table be interpreted in terms of linear regression?
Linear regression aims to find a line that best fits the data points. In this case, it would attempt to find a straight line that closely approximates the pattern of the given points. As the points in the table form a negative correlation, the line of best fit would have a negative slope.
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?
As mentioned before, since the points form a negative correlation, the slope of the line of best fit would be negative.
In summary, the correlation between x and y is negative, the missing value of y is -13, the values in the table indicate a negative correlation in terms of linear regression, and the slope of the line of best fit would be negative.