construct a scatterplot for x,y values x 1 2 3 4 5 y 0.5 0.0 -0.5-1.0-1.5 what would be the slope of this regression line would the correlation between xand y be postive oe negative how would you interpret these data in terms of regression
7. Suppose we have a set of blood pressures with a mean of 120 Systolic, and a sample standard deviation of 20 points. Assuming a normal distribution of Systolic blood pressures, between what two values should 95% of all Systolic blood pressures lie? Show all work.
To construct a scatterplot for the given x and y values, you need to plot the points on a graph. Here's how you can do it:
1. On a graph paper or using a graphing software, create a coordinate plane with the x-axis and y-axis labeled.
2. Plot the given x and y values as points on the graph. For example, the first point would be (1, 0.5), the second point would be (2, 0.0), and so on.
3. Connect the points with a line to create the scatterplot. It is likely that the points will not form a perfectly straight line.
Now, let's move on to analyzing the scatterplot. To determine the slope of the regression line, you need to perform a linear regression analysis.
To calculate the slope, you can follow these steps:
1. Calculate the means of the x and y values.
- x̅ = (1 + 2 + 3 + 4 + 5) / 5 = 3
- y̅ = (0.5 + 0.0 + (-0.5) + (-1.0) + (-1.5)) / 5 = -0.5
2. Calculate the differences between each x value and the mean of x (x - x̅) and the differences between each y value and the mean of y (y - y̅). Calculate the product of these differences.
- (x - x̅): (-2, -1, 0, 1, 2)
- (y - y̅): (1, 0.5, 0, -0.5, -1)
3. Calculate the sum of the product of differences.
- Σ[(x - x̅)(y - y̅)] = (-2 x 1) + (-1 x 0.5) + (0 x 0) + (1 x -0.5) + (2 x -1) = -4
4. Calculate the sum of squared differences for x.
- Σ[(x - x̅)^2] = (-2)^2 + (-1)^2 + (0)^2 + (1)^2 + (2)^2 = 10
5. Calculate the slope of the regression line.
- Slope (b) = Σ[(x - x̅)(y - y̅)] / Σ[(x - x̅)^2] = -4 / 10 = -0.4
Based on the calculated slope of -0.4, we can say that there is a negative relationship between the x and y variables.
Now, let's interpret the data in terms of regression. Since the slope is negative, it means that as the x values increase, the y values tend to decrease. This indicates a negative correlation between x and y.
It's worth noting that the correlation coefficient (r) would provide a more precise measure of the strength and direction of the correlation between x and y. To calculate the correlation coefficient, you would need to use the covariance and standard deviation of both x and y.