Construct a scatterplot for the (x, y) values below, and answer the following questions. You do NOT need to submit your scatterplot with your answer; however, show all other work.

x y
1 2.5
2 5.0
3 7.5
4 10.0
5 12.5







- What would be the slope of this regression line?
- Would the correlation between x and y be positive or negative?
- How would you interpret these data in terms of linear regression?

To construct a scatterplot for the given (x, y) values, you would need to plot each pair of x and y values on a graph. The x values will form the horizontal axis, while the y values will form the vertical axis.

Plotting the given data points:
(x, y) values:
(1, 2.5)
(2, 5.0)
(3, 7.5)
(4, 10.0)
(5, 12.5)

After plotting these points, you would connect them with dots to form a scatterplot. The x values will be on the horizontal axis, and the y values on the vertical axis.

To answer the questions:

1. What would be the slope of this regression line?
To find the slope of the regression line, you would need to calculate the formula for a linear regression line using the given data points. The formula for the slope of a regression line is given by:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

where n is the number of data points, Σ represents summation, (xy) represents the product of x and y, (x^2) represents the square of x, and Σx and Σy represent the sum of all x and y values, respectively.

In this case, n = 5, Σx = 15, Σy = 37.5, Σ(xy) = 77.5, and Σ(x^2) = 55.

Substituting these values into the formula, we get:

slope = (5 * 77.5 - 15 * 37.5) / (5 * 55 - (15)^2)
= (387.5 - 562.5) / (275 - 225)
= -175 / 50
= -3.5

Therefore, the slope of the regression line in this case is -3.5.

2. Would the correlation between x and y be positive or negative?
The correlation between x and y can be determined by looking at the pattern of the scatterplot. If the scatterplot shows a decreasing relationship between x and y, where as x increases, y decreases, then the correlation would be negative. Conversely, if there is an increasing relationship between x and y, then the correlation would be positive.

Looking at the given scatterplot, we can observe that as x increases, y also increases. Therefore, the correlation between x and y is positive.

3. How would you interpret these data in terms of linear regression?
Based on the scatterplot and the calculated regression line slope, we can interpret these data in terms of linear regression as follows:

- As x increases, there is a negative linear relationship with y. This means that as x increases, y tends to decrease, which is the opposite of what we observed in the scatterplot.

- The calculated slope of -3.5 indicates that for every 1 unit increase in x, there is an expected decrease of 3.5 units in y.